Quantum-inspired superposition and nonseparable states of reconfigurable metasurfaces in classical systems

Domain: physics
Published: 2025-12-09
Editorial outcome: major_revision

Abstract
Classical and quantum bits serve as cornerstone in information science. As this field rapidly evolves, the interplay between the two continues to enrich and inspire each other. Here, analog superposition states and analog nonseparable states are theoretically explored and experimentally demonstrated in a reconfigurable time-varying metasurface. To implement the quantum-inspired states in classical system, we have developed a reconfigurable metasurface capable of synthesizing analog superposition states across the temporal dimension and analog nonseparable states across spatial and polarization dimensions. Due to its unique features of analog superposition and non-separability, the proposed metasurface holds great potential to revolutionize the information processing capabilities beyond those offered by the classical information metasurface. This work not only offers a reconfigurable physical platform to advance classical and quantum information, but also will both enable unknown wave phenomena and provide promising perspectives in the fields of information science, quantum physics and material science.

Introduction
In recent years, the rapid advancement of quantum mechanics1–3 has attracted increasing attention to the field of quantum information science4–6. As an interdisciplinary discipline bridging quantum physics and information science, quantum information science is transforming research paradigms in both science and technology with its substantial practical potential and unique capabilities. Specifically, quantum communication7–10 leverages the phenomenon of quantum entanglement to ensure the security of information communication, whereas quantum computation11–14 exploits the principle of quantum superposition to achieve computational power that surpasses that of classical computers, thereby driving transformative advances in fields of materials science, chemistry, and beyond. Furthermore, the recent progress in quantum sensing15–18 and measurement19–21 technologies has significantly improved the performance of traditional sensors and measurement systems to unprecedented levels.

The success of quantum information science has not only stimulated the flourishing of quantum optics22,23, but has also propelled the development of quantum metasurfaces24–27. Metasurfaces are planar artificial structures composed of subwavelength meta-atoms arranged in either periodic or aperiodic configurations28–32. However, most passive metasurfaces lack the capability to reconfigure their electromagnetic (EM) functionality once fabricated33,34, which significantly limits their practical applications. To address this challenge, the concept of reconfigurable metasurfaces35–38 has been introduced. The switching capabilities of the EM response in reconfigurable metasurfaces have motivated the development of the digital metasurfaces39 and subsequently evolved into information metasurfaces40–48, which serve to bridge information science and classical EM physics.

The basic information-processing units of information metasurfaces are based on classical digital bits, which offer benefits such as stability, ease of storage and transmission, and operational simplicity. However, they suffer from limitations in information capacity and parallel-processing capability. In contrast, quantum bits (qubits)49–51 exhibit unprecedented superiority in these aspects, offering potential solutions to address the challenges currently faced by classical digital bits. However, qubits are often unstable, difficult to store and transmit, and highly susceptible to environmental interference. To combine the respective advantages of classical bits and qubits, several attempts are being made to develop quantum-inspired bits52,53 in classical systems. Nevertheless, current studies are mostly limited to theoretical explorations, and the experimental realization and manipulation of quantum-inspired states in classical systems remain a significant challenge in this field.

In this work, we investigate the quantum-inspired states of reconfigurable metasurfaces to emulate the mathematical and geometrical representations of the quantum states. We should clarify that the quantum-inspired states discussed here are implemented in a classical system rather than in a quantum system. Generally, the mathematical representation provides a theoretical framework to rigorously describe the quantum-inspired states, whereas the geometric representation offers an intuitive way to understand them. Specifically, we initiate our discussions by introducing the concept and mathematical framework of the analog superposition state to explore the analog superposition behavior of the EM waves based on a reconfigurable metasurface in a classical system. To validate the correctness of our theoretical model, we perform numerical simulations on the reconfigurable time-varying metasurface. All numerical simulations were conducted based on the fundamental frequency, without considering the influence of other harmonic frequencies. Each meta-atom on the metasurface can be individually controlled through mechanical rotation, thereby enabling flexible manipulation of the polarization state on the Poincaré sphere. Notably, the reconfigurable feature of the reconfigurable time-varying metasurface allows it to transform the polarization state by reaching all possible points on the Poincaré sphere, which is a crucial ability to implement the analog superposition state. We further demonstrate an analog nonseparable state that mirrors the entanglement between light spin and far-field spatial modes. In a proof-of-concept experiment, we show excellent agreement between the experimental results and numerical simulations, thus affirming that the proposed reconfigurable time-varying metasurface is a feasible platform to realize the concept of quantum-inspired states. We believe that the introduction of the quantum-inspired bit and the realization of the reconfigurable array platform will advance the developments in various fields, including quantum physics, information science, and metamaterials.

Results
Reconfigurable time-varying metasurface
We commence our analysis by investigating the EM properties of various meta-atoms to explore the correlations among different information bit types. In classical information processing, a classical bit is generally represented by the binary state 0 or 1. Physically, these classical bits are inherently binary systems, distinguished by their exclusive occupation of one of two possible states. The EM properties of the meta-atom in the classical information metasurfaces are controlled by a binary state, namely the coding state 0 (ON) or 1 (OFF), by switching the PIN diode, as depicted in Fig. 1a. Mathematically, the binary state can be formulated as |Ψ〉=(1−δ)|0〉+δ|1〉, where |0〉 and |1〉 denote the respective reflection polarization states (i.e., |Ψ〉) of the meta-atom when the PIN diode is in its ON (δ=0) and OFF (δ=1) configurations, with δ being restricted to 0 or 1. It is noteworthy that the operations involving the classical bits are deterministic, complying with Boolean algebra principles. In the classical context, the classical bits are limited to process a single state at any given moment. In contrast, the quantum bits leverage the superposition property to provide significant advantages in parallel information processing. Generally, the Bloch sphere is used as a geometric representation to succinctly and clearly convey this concept, as depicted in Fig. 1b. In this representation, the state of a quantum bit can be visualized at any location on the Bloch sphere, transcending the limitations of classical information processing.

The mathematical representation of a quantum bit can be expressed as a linear superposition of two polarization states, namely |Ψ〉=α|0〉+β|1〉. The coefficients, α and β, are complex numbers that are subjected to normalization and probabilistic constraints |α|2+|β|2=1. After initializing the global phase to zero and defining the relative phase as ϕ, the state |Ψ〉 has only two degrees of freedom. The Bloch sphere surface, which represents the qubit state space, is inherently two-dimensional, providing two distinct local degrees of freedom. As a result, this state can be mathematically represented by |Ψi= cosθ|0i+eiϕ sinθ|1i. In this context, the polar angle θ (ranging from 0 to π) and the azimuthal angle ϕ (from 0 to 2π) correspondingly denote the quantum bit’s position on the Bloch sphere, akin to the latitude and longitude. With the determination of θ and ϕ, the quantum state is fully defined and can be geometrically represented.

Inspired by the mathematical and geometric representations of quantum bits, here we introduce a concept of quantum-inspired bits (as shown in Fig. 1b), the state of which can be mathematically expressed as an analog superposition state:
|Ψi= cosθ|Ri+eiϕ sinθ|Li. Here, |R〉 and |L〉 represent two orthogonal bases that constitute the bit: right-handed circular polarization (RCP) and left-handed circular polarization (LCP) states. This mathematical representation is applicable to the RCP plane-wave incidence scenarios. For the LCP incidence, the coefficients associated with two orthogonal bases should be interchanged.

To implement the aforementioned analog superposition state, we propose a reconfigurable time-varying metasurface as a feasible physical platform. Additionally, the metasurface exhibits analog nonseparable state properties, as shown in Fig. 1c. Different from the conventional digital coding metasurface, the proposed reconfigurable time-varying metasurface employs a discrete periodic configuration of meta-atoms, which are designed to overcome the rotation-related challenges, including friction and collisions between adjacent meta-atoms. We employ a multi-layered metal-insulator-metal spacer structure to design the meta-atom, optimizing their performance, and integrate stepping motors for actuation (details can be found in the “Methods” section), as illustrated in Fig. 1d. This structure facilitates the flexible control of the reflected wave’s polarization state over the Poincaré sphere through both forward and backward stepping and rotational stepping dimensions in practice. Given that the analog superposition state corresponds to the polarization state of the reflected wave, we opt to represent this using the Poincaré sphere rather than the Bloch sphere, as shown in Fig. 1b for more accurate visualization. We note that the realization of this concept essentially relies on the introduction of a temporal dimension and rotational transformations in the same reconfigurable time-varying meta-atom. In quantum physics, a qubit has an instant superposition of states. In our case, the analog superposition of states is implemented in a certain time interval on the reconfigurable time-varying meta-atom by manipulating its rotation angle at different times. It is important to emphasize that both the time interval and the system’s response time remain on the order of milliseconds. In principle, minimizing the time interval towards zero would yield an analog of the qubit superposition state. More details of the theoretical derivations for the mathematical and geometric representations of the analog superposition state in reconfigurable time-varying metasurfaces can be found in the Supplementary Note 1.

Reconfigurable time-varying meta-atom
The configuration of the reconfigurable time-varying meta-atom is illustrated in Fig. 2a. The metal patch of the third layer includes a pair of arcs and a rectangular strip, while the metal patches of the first and fifth layers feature a pair of symmetric arcs. Additionally, these layers are equipped with stepping motors to effectively control the three-layer insulator structure (see Fig. 2c). To avoid friction and collision during rotation, we designed the insulator to be circular, with a diameter slightly smaller than the edge length of the square metal backplate. This design dimension is adequate to meet the requirements for the stepper motors to drive the rotation of each insulating layer. Due to the total reflection characteristics of the metallic backplane, the impact of the motor on the unit characteristics can be neglected.

The rotational angles of two layers with respect to the rectangular strip are γ1 and κ1, respectively (see more details in the “Methods” section). When γ1 is set equal to κ1, the structure becomes centrosymmetric, permitting it to rotate around its central axis of symmetry. The designed meta-atom achieves highly efficient polarization conversion by exploiting strong anisotropy and limits the internal resonance field to minimize the coupling between adjacent units. Theoretically, a rotation of the meta-atom around its central axis, perpendicular to the z-axis by an angle α (as depicted in Fig. 2b), would result in a phase change of the reflection coefficients RRR and RLL. Based on the Pancharatnam-Berry (PB) phase theory, this phase change is equal to 2α. Here, RRR and RLL represent the reflection coefficients for RCP and LCP incident waves converted to their corresponding co-polarization reflected waves, respectively, and α denotes the overall rotation angle of the meta-atom.

To assess the reflective capabilities of the proposed reconfigurable time-varying meta-atom under a linearly polarized incident wave, numerical simulations are performed. Supplementary Fig. 19b, c illustrates the simulated amplitude and phase responses of the reflection coefficients RUU, RUV, RVU, RVV of the reconfigurable time-varying meta-atom (see Supplementary Fig. 22a) with γ=κ=90°, γ1=κ1=0°, and α=0° in the frequency range from 1 to 8 GHz. Here, reference coordinates {U, V} denote the principal axes of the local coordinate systems of the meta-atom, and Rij signifies the complex reflection amplitude for the incoming EM waves with linear polarization along the j-axis and the outgoing waves with linear polarization along the i-axis, where i, j ∈ {U, V}. The elements of the Jones matrix R(0) are not entirely independent but are constrained by the symmetry of the meta-atom54. According to group theory, if a structure is invariant under a particular symmetric operation characterized by operator G, then the matrix R(0) will also be invariant under this operation, mathematically expressed as GR(0)G−1=R(0). Considering that the meta-atom has mirror symmetry with respect to its principal axis, we have the matrix G = [1 0; 0 -1], which necessitates that RUV=RVU=0, as verified by Supplementary Fig. 22b, c. In addition, the system studied in our work exhibits time-reversal symmetry, and the proposed reconfigurable time-varying meta-atom is mirror-symmetric. Based on the law of energy conservation, it can be inferred that the coefficients RUU and RVV are approximately equal in magnitude.

The meta-atom displayed in Supplementary Fig. 22a undergoes 135° counter-clockwise rotation around the z-axis, resulting in the transformation of the incident plane wave from linear to circular polarization, as shown in Fig. 2d. Following this, we further study the reflection responses of the proposed meta-atom. Figure 2e and Supplementary Fig. 19d showcase the theoretically predicted results and numerically simulated results of the reflection coefficients RRR, RLR, RRL, RLL. We remark that the theoretically predicted results are based on analytical values derived from the Jones matrix transformations, as detailed in Supplementary Note 13, whereas the numerically simulated results are obtained by using the full-wave simulations. The simulated amplitudes and phases are depicted with crimson and azure lines, respectively, and the theoretical estimations for amplitudes and phases are indicated by red squares and blue diamond dots. We observe that there is agreement between the theoretical calculations and numerical simulations.

The Poincaré sphere enables a straightforward depiction of all possible polarization states. Each point on the sphere represents a specific polarization state, where the north and south poles indicate the right-circular polarization (|RCP〉) state and left-circular polarization (|LCP〉) state, respectively. The points along the equator illustrate the linear polarization (|LP〉) states, and those elsewhere indicate elliptical polarization (|EP〉) states. The Poincaré sphere provides an insightful visualization of the evolution process of the polarization from one state to another. As shown in Fig. 2f, under the illumination of an RCP plane wave, the reflected field is numerically calculated to trace the transformation trajectory of polarization on the Poincaré sphere. In the incident region, the polarization state of the EM wave remains RCP along the whole incident propagation path. This state is referred to as the initial state, which is marked with a red circle on the Poincaré sphere in Fig. 2g.

In the reflected region, the incident EM wave interacts with the reconfigurable time-varying meta-atom, leading to significant changes in polarization state. This reflected polarization state gradually evolves along the reflected propagation path and eventually settles into a stable state. We define this stable polarization state as the final state, depicted with a purple dot on the Poincaré sphere. The transition of the polarization state of the reflected wave is visualized with a sequence of smaller red dots, each of which represents a specific transition state. In Fig. 2f, we present the polarization state of the reflected wave at eight equidistant positions to better illustrate the polarization evolution. The theoretical values of the final state of the reflected wave are further derived using Eq. (S3) or (S5). These values are represented with a green circle on the Poincaré sphere. The strong alignment between the purple and green circles further confirms the validity of our geometric representation of the proposed theory of analog superposition states in reconfigurable time-varying metasurfaces. While our research primarily focuses on the final polarization state in the far field, the polarization transformation in the near field is also very helpful for gaining a deeper understanding of the physics behind how the proposed metasurface works55,56. Additionally, we examine the polarization evolution under LCP plane wave incidence, as demonstrated in Fig. 2h, i, and determine the expected final state using Eq. (S4) to enhance the reliability.

In order to ensure the reliability and accuracy of the analog superposition state in mathematical and geometric representations, we conducted a wideband validation at multiple frequency points. This approach aims to overcome the inherent limitation in the geometric representation of the analog superposition state on the Poincaré sphere, which is defined to analogously mimic the superposition state properties of a quantum bit at a single frequency point. Here, we should note that the Poincaré sphere is capable of representing polarization states across multiple frequencies, with each point on the sphere corresponding to a polarization state at one frequency. This enables the characterization of a spectrum of polarization states. From an application perspective, the analog superposition states in the proposed reconfigurable time-varying metasurface are expected to be effective over a wide frequency spectrum, rather than being limited to one specific frequency point. Further details on the broadband validation of the analog superposition state are available in the Supplementary Note 12. Supplementary Fig. 16a, d shows the conceptual diagrams of the reconfigurable time-varying meta-atoms under the RCP and LCP plane-wave incidences, showcasing the polarization evolution path on the Poincaré sphere at an observation frequency of 5.35 GHz. It should be noted that the meta-atom and observation frequency in this scenario are consistent with those in Fig. 2f–i. We initially examined the circularly polarized reflection responses of the meta-atom by obtaining the theoretically predicted and numerically simulated results for the amplitude-frequency and phase-frequency responses, as shown in Supplementary Fig. 16b, c, e, f. Subsequently, we compare four reflection coefficients in the range from 1 to 8 GHz for the purpose of wideband validation, which are demonstrated in the histograms in Supplementary Fig. 16g–j.

Based on the mathematical values of the reflection coefficients, we display the geometric representation of the reflected polarization’s final state under RCP and LCP illuminations, as demonstrated in Supplementary Fig. 17a, c (see the Supplementary Note 13 for the calculation formula). Meanwhile, we visually demonstrate the reflected polarization evolution paths on the Poincaré sphere in Supplementary Fig. 17b, d, where the theoretically predicted results and numerically simulated results of the reflection polarization’s final states are compared with the purple and green dots. The comparison of the results confirms the applicability and accuracy of both mathematical and geometric representations of analog superposition states in the proposed reconfigurable time-varying metasurface, supporting the reliability and effectiveness of the proposed approach.

Analog superposition state of reconfigurable metasurfaces in classical systems
As the fundamental units of information in quantum information theory, the quantum bits exhibit two primary features: superposition57 and entanglement58,59. Drawing inspiration from the distinct representation of the quantum-bit superposition states on the Bloch sphere, here we study the analog superposition state in the proposed reconfigurable time-varying metasurface on the Poincaré sphere (with built details provided in the Supplementary Note 1). Equations (S3) and (S4) demonstrate that the polarization state of the EM waves reflected by a reconfigurable time-varying metasurface is determined by two degrees of freedom on the Poincaré sphere, namely θ and ϕ, as illustrated in Fig. 1d. Under the excitation of circularly polarized plane waves, we find that the resonant frequency of the reconfigurable time-varying metasurface shifts towards lower frequencies as the equivalent arc length of the meta-atom increases. Here, the equivalent arc length refers to the longer arc distance between the ends of the first and fifth curved metallic layers with respect to the central longitudinal axis of the third rectangular strip, with their numerical values given by (γ1+γ2)/2 and (κ1+κ2)/2, respectively.

As a result, by maintaining a constant overall rotation angle α and adjusting the relative rotation angles γ1 and κ1, it is feasible to achieve a complete transition of |RRR| from 1 to 0, while keeping fRRR unchanged at a specific frequency. This feature enables a flexible scanning of the polarization states along the latitude of the Poincaré sphere with the latitude angle θ from 0 to π while keeping the longitude angle ϕ constant, as shown in Fig. 3a, e. The agreement between full-wave simulations and theoretical predictions is validated in Fig. 3c, g (see more details of the result comparison in Supplementary Table 1). This also makes it possible to flexibly manipulate the analog superposition state of the reconfigurable time-varying meta-atom along the latitude of the Poincaré sphere by maintaining its rotation angle α=0° and tuning the relative rotation angles (γ1 and κ1) within a certain range, as depicted in Fig. 3a and Supplementary Fig. 23.

Since the reconfigurable time-varying meta-atom is designed from the PB phase, one can control the polarization evolution path of the reflected wave by manipulating the overall rotation angle α of the meta-atom. Our results show that the PB phase is only dependent on the rotation angle of the meta-atom and can achieve a phase coverage from 0 to 2π. We also find that the reflected wave generated by the reconfigurable time-varying metasurface can induce a longitude-angle change (Δϕ) on the Poincaré sphere, namely Δϕ=±2Δα. Hence, when the equivalent arc length of the meta-atom structure remains the same, the longitude angle ϕ can traverse from 0° to 360° by adjusting the rotation angle α from 0° to 180°, whilst maintaining the latitude angle θ constant.

To support our findings, we have conducted both numerical simulations and theoretical predictions, as shown in Fig. 3d, h. The excellent agreement between the numerical simulations and theoretical predictions of the final polarization states of reflected waves generated by a metasurface composed of periodically arranged meta-atoms under circularly polarized excitation confirms the accuracy of the proposed theory (see more numerical data in Supplementary Table 2). It merits emphasis that our theory is based on linear polarization, whereas the simulations directly pertain to circular polarization, indicating a distinction between the roots of the two. Moreover, the theory offers a swift and exceedingly precise analytical method unmatched by simulations for determining the final polarization state on the Poincaré sphere. This method not only avoids the complications associated with electric field simulations and subsequent processing (as depicted in Supplementary Fig. 1) but also simplifies experimental assessments and analytical processes. Furthermore, by adjusting the overall rotation angle α and fixing the relative rotation angles (γ1 and κ1) of each reconfigurable time-varying meta-atom, we can map the final polarization state of the reflected wave along the latitude lines on the Poincaré sphere, as illustrated in Fig. 3b, f and Supplementary Fig. 24a, b. Due to the inherent tunability of the proposed meta-atom, the reconfigurable time-varying meta-atom can have infinite rotation configurations. Under a given rotation configuration, the EM response (i.e., the final polarization state of the reflected wave) of the meta-atom will always be mapped to a specific point on the Poincaré sphere. To realize the analog superposition state in the proposed reconfigurable time-varying metasurface, it is crucial to traverse all possible polarization states on the Poincaré sphere. By manipulating the rotation configuration of the proposed meta-atom, we can flexibly scan the final polarization states of the reflected wave across the Poincaré sphere’s longitude and latitude. This allows us to construct the analog superposition states on the proposed reconfigurable time-varying metasurface. It should be noted that the analog superposition states have been explored and validated under the condition of normal incidence with circularly polarized waves. A detailed discussion on the impact of different polarizations and incidence angles on the performance of the analog superposition states is presented in the Supplementary Note 7.

Analog nonseparable state of reconfigurable metasurfaces in classical systems
Entanglement is a distinctive phenomenon in quantum mechanics, including the inter-system entanglement and intra-system entanglement. Both types of entanglement are characterized by the non-separable connection between states. In the classical systems, it is not feasible to achieve the inter-system entanglement. In contrast, the intra-system entanglement can be explored in the classical systems by investigating the inseparability among various degrees of freedom in a single system, and it is well-known as the classical entanglement.

To characterize the analog nonseparable states of space-polarization60,61 in the proposed reconfigurable time-varying metasurfaces, we study different degrees of freedom (such as the polarization and spatial modes) in EM systems to demonstrate the analog nonseparable correlation. Due to the spin-conjugate symmetry of the left- and right-handed PB phases, we can establish an analog nonseparable state based on the reconfigurable time-varying meta-atom. We further introduce the concept of coding metasurface, wherein the coding inseparability always maintain a mutual correlation between the coding patterns of both spin states, as illustrated in Fig. 4a, c. A detailed examination of the structures, phases, and amplitude responses for four meta-atoms applied in 2-bit encoding is presented in Supplementary Fig. 2. Essentially, the meta-atoms remain unchanged in parameters, leading to uniform amplitude responses. In terms of phase differences, the reconfigurable time-varying meta-atoms assign the phase coding states of 0, 1, 2, and 3 to the spin-up ∇+90°|R〉 and spin-down ∇−90°|R〉. Inversely, the coding states of 3, 2, 1, and 0 are naturally assigned to the spin-down ∇−90°|L〉 and spin-up ∇+90°|L〉, respectively, as shown in Supplementary Fig. 2c, d.

Illuminated by the incident EM wave with horizontally linear polarization, the scattering field patterns of the reconfigurable time-varying meta-atoms exhibit an analog nonseparable state between the spin (polarization) and far-field spatial modes, as shown in Fig. 4b, d. For coding pattern 1, the beams corresponding to the spin-up and spin-down states occur at the spatial modes (11.0°, 0°) and (−11.0°, 180°), which are exactly aligned with the theoretical prediction results of (11.0°, 0°) and (−11.0°, 180°). Coding pattern 2 demonstrate similar results. In addition, the calculated Schmidt numbers (K) for both cases are 2, indicating that the polarization (spin) and spatial modes reach the maximum entanglement degree. Hence, we validate that an analog nonseparable state between the spin and far-field spatial modes can be implemented in the reconfigurable time-varying meta-atoms. Moreover, the resultant spin splitting phenomenon can be interpreted as a classical EM wave analog of the spin Hall effect.

Experimental demonstration of reconfigurable time-varying metasurfaces
To experimentally demonstrate that the proposed reconfigurable time-varying metasurface is capable of characterizing the analog superposition state to yield an analog of the qubit superposition state, we fabricate a reconfigurable time-varying metasurface by setting γ=κ=90°. More details of these devices and their associated testing procedures are provided in the “Methods” section. Figure 5b, c presents the polarization conversion efficiencies and the positions (θ, ϕ) of the final polarization states of the reflected waves on the Poincaré sphere for different samples (see Fig. 5a) in a broad frequency band, respectively. Meanwhile, the corresponding geometric representations at a specific frequency of 5.33 GHz are depicted in Fig. 5d.

As verified in Fig. 5c, there is a notable concordance between the numerically simulated and experimentally measured results, regardless of the same rotation angle with different equivalent arc lengths (samples 1 and 2), or different rotation angles with the same equivalent arc lengths (samples 1 and 3). Such an agreement provides more reliable evidence to validate the accuracy of the mathematical and geometric representations for the analog superposition state in a reconfigurable time-varying metasurface. It should be noted that while our reconfigurable time-varying metasurface demonstrates effectiveness based on a mechanical modulation approach, the modulation speed is inherently dependent on the performance of the motors used (i.e., on the millisecond scale). In practical applications, as the complexity of the applications increases, we may not be limited to the analog superposition states or analog nonseparable states at a single frequency, leading to a heightened demand for increased modulation speeds. In fact, the existing literature has reported various faster modulation methods, such as electrical or optical tuning approaches. However, realizing the concept of the quantum-inspired bits requires to meet four necessary conditions, which cannot be achieved by the current reports. Therefore, in this initial attempt, we just realized the functionality. For a more detailed comparison between this work and the related studies, please refer to Supplementary Note 17. This section only includes experimental results for three cases. Additional experimental results and more relevant discussions (including the polarization conversion efficiency, signal-to-noise ratio (SNR), and fidelity) are provided in the Supplementary Notes 8 and 9. Furthermore, we provide a more detailed experimental strategy to achieve more flexible control in the Supplementary Note 16.

Methods
Meta-atom design and metasurface fabrication
Our proposed reconfigurable time-varying metasurface is structured with separately and periodically arranged meta-atoms. The characteristics of these meta-atoms are optimized through rigorous numerical simulations and experimental evaluations. The geometric parameters of these meta-atoms are detailed in Fig. 2.

The metallic structure was fabricated by using printed circuit board (PCB) techniques. The F4B dielectric substrate used in this construction is circular and has three insulating layers. The thicknesses of the layers are h=3mm, h1=h2=0.254mm. The substrate has a radius of R1=9.7mm and a relative permittivity of 2.65. With a notably low loss tangent of 0.001, the substrate ensures optimal performance. The substrate is mounted atop a square and metallic plane with periodic side lengths of p=20mm. The construct is designed with multi-layered metallic motifs on the surface and a foundational backplate made of copper. The thickness of each layer is 18μm. The third layer hosts an array of metallic patches, each with an outer radius of R=4.6mm and an inner radius of 3.3mm. The geometrical parameters of the metal patches in the first- and fifth-layers mirror those of the arc segments in the third layer, while the rectangular strip width matches the arc width. Meta-atoms are arranged with center-to-center spacings of 20mm along both the x and y axes, maintaining a minimum gap of 0.6mm between them. Such a configuration allows for the free rotational movement of each meta-atom. Furthermore, each meta-atom is equipped with a motor for rotation control. The optimized dimensions of the meta-atoms fully accommodate the spatial requirements for independent rotational control of the insulating layers corresponding to each stepper motor. In the experimental setup, the prototype metasurface was constructed, comprising a matrix of 576 individually rotatable meta-atoms. The expansive metallic backplane covers an area of 570×560mm2. We also provide a detailed fabrication approach and corresponding experimental strategy in the Supplementary Note 16 for further research and applications.

Simulations
Rigorous numerical simulations throughout this study were performed using commercial software, CST Microwave Studio. In the mechanical modulation approach employed here, the control speed is much lower than the EM wave propagation speed. Thus, this scenario can be treated as a quasi-static EM problem. Consequently, in the numerical simulations, both analog superposition states and analog nonseparable states of the quantum-inspired bits synthesized in the time dimension were treated as static, eliminating the need for time-varying modeling. The analog superposition properties of the meta-atoms were numerically simulated using their frequency-domain solver. The simulations were conducted by imposing unit cell boundary conditions along the x and y axes, while using open-space boundary conditions along the z-axis. Meanwhile, the time-domain solver was employed to investigate the analog nonseparable state in a reconfigurable time-varying metasurface, which was simulated by applying open boundary conditions in all three axes (x, y, and z). It should be noted that the analog nonseparable state simulation featured in Fig. 4 is operated at a frequency of 9.80 GHz. The dual coding patterns illustrated in Fig. 4a, c, were periodically structured in the x-axis, while preserving a fixed orientation along the y-axis. Each coding element is structured as a supercell composed of two identical units, resulting in a periodicity denoted as Γ, spanning a distance of 160mm.

Experiments
The experimental system is demonstrated in Supplementary Fig. 3a, where the fabricated metasurface is housed in a compact microwave anechoic chamber. The measurement system includes two identical linearly polarized broadband horn antennas (GJ-WRDHA-U8/08-N) and a vector network analyzer (VNA) (Agilent N5230C). The two antennas are connected to the two ports of the VNA, serving as the feeding and receiving terminals, respectively. These two antennas are aligned at oblique angles of ±5° to measure the normal reflected EM waves, as shown in Supplementary Fig. 3b. Antennas are placed 1m distant from the metasurface. The reflection coefficients ruu, ruv, rvu, rvv of the two metasurface prototypes were carefully measured at different rotational angles by using the time-domain gate innovations provided by the VNA. Transformation calculations predicated on Eqs. (S3) and (S4) were executed to obtain test results for θ and ϕ at each rotational angle. These methodologies contribute to an in-depth understanding of the reflective characteristics of the proposed reconfigurable time-varying metasurfaces.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper presents a classical/quantum qbits controlled by time modulation metasurfaces. The authors use mechanical\nparadigms to rotate and modulate the elements.\n- mechanical rotation while efficient, as authors mentioning, they are low in speed? How the authors want to achieve such\nrotation in practice?\n- What is resolution? Given metasurfaces elements and pitch size, is it enough to put required elements for rotation?\n- Does sped of rotation affect the modulation?\n- How is it modeled? Time modulation? Is it full wave modeling from f0 to sideband creation by modulation?\n- How the authors want to fabricate this? (it seems very complicated and several practical maters need to be addressed)\n- Not all relevant references have been addressed", "reviewer_2": "In the submitted manuscript “Superposition and nonseparable states in reconfigurable time-varying metasurfaces”, Long\nChen et al. have reported on the realization of the analog of quantum bits(qubits) in classical systems, which referred to\n“intermediate states” between the classical and quantum bits in the manuscript. To explore the superposition and\nnonseparability of the intermediate states, the authors have designed a mechanically controlled time-varying metasurface,\nby which they rotate the relative angle of three layers of each isolated meta-atoms, thus modulating metasurface’s response\nto incident left- (LCP) and right- (RCP) handed circularly polarized electromagnetic waves. For the proposed system, |LCP>\nand |RCP> play the role akin to quantum states |0> and |1> states, and form a pair of orthogonal bases that constitute the bit.\nIn other words, for any states |ψ>, they can be expressed as the superposition of |LCP> and |RCP>, that is |ψ> = cos(θ/2)\n|RCP> + eiϕ sin(θ/2) |LCP>. But differently, in the classical system, the geometrical presentation of qubits is on the Poincaré\nsphere rather than the Bloch sphere, and θ (ϕ) is the polar (azimuthal) angle. Intuitively, |ψ> reveals the polarization of output\nstates of the metasurface, which can cover the whole Poincaré sphere by dynamically modulating the metasurface. Further,\nthe authors have performed experiments to validate the superposition and the polarization-spatial nonseparability of\nintermediate states, which agree well with the theoretical analysis and simulations.\nIn my opinion, this work is impressive and I believe it makes significant contributions to the fields of information science,\nquantum physics, and material science. Of course, one of the most immediate applications can be real-time arbitrary\npolarization conversion. The manuscript is also well-written and logically organized.\nIn summary, I consider this work to be valuable and recommend it for publication in Nature Communications.\nFinally, I am curious about the response time of the system, and it would be great if the author could give more details."}, "author_response": "REVIEWER #1\nWe sincerely appreciate Reviewer #1 for the time and effort invested in reviewing our\nmanuscript and offering a wealth of insightful comments and thoughtful suggestions. These\ncomments and suggestions are extremely valuable to enhance the quality of our manuscript.\nFollowing the reviewer’s constructive guidance, we have carefully revised the paper to improve\nits clarity and comprehensibility.\nComment 1.1: Mechanical rotation while efficient, as authors mentioning, they are low in speed? How\nthe authors want to achieve such rotation in practice?\nResponse: Thank you for your good questions. The core focus of this work is introducing the\nconcept of quantum-inspired bits, and the designed reconfigurable platform is primarily\nintended for the validation of this concept, with all experiments serving as proof-of-principle\nverification. Consequently, we employed a relatively simple and easily implementable method\nfor mechanical modulations using motors. While this approach has proven efficient, it does\nindeed suffer from limitations in speed, primarily constrained by the maximum rotational speed\nof the motors (typically in the millisecond range). We recognize that achieving a faster\nmodulation speed is crucial for realizing true quantum-inspired bits, which represents a\nsignificant challenge that we aim to address in the future. Looking ahead, we plan to expand\nthis conceptual validation platform to include faster modulation methods such as electrical and\noptical modulations, in order to meet the increasingly complex application requirements. We\nbelieve that this will open new possibilities for more efficient quantum information processing.\nAction Taken: In accordance with your comments, we have provided a detailed explanation of\nthe aforementioned points in the revised manuscript, especially regarding to the future outlook.\nThe specific revisions are as follows:\n[Reconfigurable time-varying metasurface]\n… We employ a multi-layered metal-insulator-metal (MIM) spacer structure to design the meta-\natom, optimizing their performance, and integrate stepping motors for actuation (details can be\nfound in the Methods and Supplementary Materials sections), as illustrated in Fig. 1d. This\nstructure facilitates the flexible control of the reflected wave’s polarization state over the\nPoincare sphere through both forward and backward stepping and rotational stepping\ndimensions in practice. …\n[Reconfigurable time-varying meta-atom]\nThe configuration of the reconfigurable time-varying meta-atom is illustrated in Fig. 2a. The\nP\nA\nG\nE\nmetal patch of the third layer includes a pair of arcs and a rectangular strip, while the metal\npatches of the first and fifth layers feature a pair of symmetric arcs. Additionally, these layers\nare equipped with stepping motors to effectively control the three-layer insulator structure (see\nFig. 2c). To avoid friction and collision during rotation, we designed the insulator to be circular,\nwith a diameter slightly smaller than the edge length of the square metal backplate. This design\ndimension is adequate to meet the requirements for the stepper motors to drive the rotation of\neach insulating layer. Due to the total reflection characteristics of the metallic backplane, the\nimpact of the motor on the unit characteristics can be neglected.\n[Experimental demonstration of reconfigurable time-varying metasurfaces]\n… It should be noted that while our reconfigurable time-varying metasurface demonstrates\neffectiveness based on a mechanical modulation approach, the modulation speed is inherently\ndependent on the performance of the motors used (i.e., on the millisecond scale). In practical\napplications, as the complexity of the applications increases, we may not be limited to the\nsuperposition states or nonseparable states at a single frequency, leading to a heightened\ndemand for increased modulation speeds. Therefore, we aim to extend this approach to\nelectrically or optically controlled high-speed modulation methods, although this may be\naccompanied by increased energy consumption. …\n[Discussion]\n… However, the mechanical modulation employed in the current reconfigurable time-varying\nmetasurface platform is entirely dependent on the performance of the motors, which limits its\noperational processing speed. As the demands for practical applications increase, the proposed\nreconfigurable time-varying metasurface should be further expanded through electrical and\noptical control methods, enabling faster modulation speeds and more complex system functions,\nsuch as analog simulations of quantum gates and quantum circuits within classical EM\nsystems. …\nComment 1.2: What is resolution? Given metasurfaces elements and pitch size, is it enough to put\nrequired elements for rotation?\nResponse: Thank you for your insightful questions. The period of the square lattice of the meta-\natoms is 20 mm, with a specific radius of the three-layer insulating layer measuring 9.7 mm.\nThe center-to-center distance between the meta-atoms along both x-axis and y-axis is 20 mm,\nmaintaining a minimum gap of 0.6 mm between them. These dimensions and spacing fully\nsatisfy the spatial requirements for the independent rotational control of the insulating layers\ncorresponding to each stepper motor.\nP\nA\nG\nE\nAction Taken: Based on your comments, we have added relevant supplementary information\nin the main text and introduced Section 15 in the Supplementary Information to provide a\ndetailed account of the stepper motors used in our work.\n[Reconfigurable time-varying meta-atom]\nThe configuration of the reconfigurable time-varying meta-atom is illustrated in Fig. 2a. The\nmetal patch of the third layer includes a pair of arcs and a rectangular strip, while the metal\npatches of the first and fifth layers feature a pair of symmetric arcs. Additionally, these layers\nare equipped with stepping motors to effectively control the three-layer insulator structure (see\nFig. 2c). To avoid friction and collision during rotation, we designed the insulator to be circular,\nwith a diameter slightly smaller than the edge length of the square metal backplate. This design\ndimension is adequate to meet the requirements for the stepper motors to drive the rotation of\neach insulating layer. Due to the total reflection characteristics of the metallic backplane, the\nimpact of the motor on the unit characteristics can be neglected.\n[Meta-atom design and metasurface fabrication]\n… Furthermore, each meta-atom is equipped with a motor for rotation control (as detailed in\nthe Supplementary Information). The optimized dimensions of the meta-atoms fully\naccommodate the spatial requirements for independent rotational control of the insulating layers\ncorresponding to each stepper motor. …\n[Section 15: Details of the stepping motor]\nThe stepping motor utilized in this work is illustrated in Fig. S19, with detailed electrical\nperformance provided in Table S1. It is noteworthy that the rotational speed of this stepping\nmotor is approximately 4000 revolutions per minute, resulting in a system response time on the\norder of milliseconds.\nTable S1. Electrical performance. The stepping motors were bought from a commercial\ncompany named Wuxi Stepping Automatic Control Technology Co., Ltd. in Wuxi, China.\nStep angle 1.8 °⁄𝑺𝒕𝒆𝒑\nRated voltage 1.92 𝑽\nCurrent 0.6 𝑨⁄𝑷𝒉𝒂𝒔𝒆\nResistance 3.2 𝛀⁄𝑺𝒕𝒆𝒑\nP\nA\nG\nE\nInductance 0.9 𝒎𝑯⁄𝑺𝒕𝒆𝒑\nHolding torque 1.4 𝑵.𝒄𝒎\nDetent torque 0.2 𝑵.𝒄𝒎\nRotor inertia 2.5 𝒈.𝒄𝒎𝟐\nMotor length 28 𝒎𝒎\nLead wire 4 𝑵𝑶\nMotor weight 50 𝒈\nFig. S19. Photo and detailed geometric parameters (mm) of the adopted stepping motor.\nComment 1.3: Does speed of rotation affect the modulation?\nResponse: Thank you for the good question. Our study is exclusively focused on phenomena\noccurring at the fundamental frequency in exploring both superposition and nonseparable states,\nwithout considering the effects of harmonics. Consequently, the investigation is conducted\nwithin a single frequency point. From this perspective, the impact of the rotational speed of the\nreconfigurable time-varying metasurface on modulation can be considered negligible. However,\nwith the future alterations in modulation methods and the increase in speed, we plan to further\ninvestigate the nonlinear effects, such as harmonic characteristics. At that stage, the rotation\nspeed may have a significant impact on the modulation.\nAction Taken: Following your valuable comment, we have added relevant explanations and\nclarifications in the revised manuscript to enhance its quality further.\n[Superposition states in reconfigurable time-varying metasurfaces]\nFig.3 | … c,d,g,h The numerical simulations and theoretical predictions of the final polarization\nstates of the reflected wave under RCP and LCP incidences, taking into account the variations\nacross two distinct dimensional modulations. Since only the superposition state at the\nfundamental frequency is considered without involving the harmonics, the impact of the\nP\nA\nG\nE\nmechanical rotation speed on the two modulations is negligible. …\n[Discussion]\n… It should be noted that both investigations of the superposition and nonseparable states at\nthe fundamental frequency do not take into account the effects of harmonics, which implies that\nthe rotational speed of each meta-atom has a negligible impact on the modulation. …\nComment 1.4: How is it modeled? Time modulation? Is it full wave modeling from f0 to sideband\ncreation by modulation?\nResponse: Thank you for your insightful questions. Currently, we use a mechanically tunable\napproach, and our control speed is relatively slow compared to the propagation speeds of\nelectromagnetic waves at the nanosecond or even picosecond level. As a result, this can be\nregarded as a quasi-static electromagnetic problem. During our simulations, we treated the\nsystem as static and did not conduct time-varying simulations. Furthermore, although our\nquantum-inspired bits are synthesized through the time dimension, this study is primarily\nfocused on the fundamental frequency 𝑓 , and thus we only simulated at this frequency without\n0\nconsidering the effects of harmonics. For further clarification, please refer to response 1.3.\nLooking ahead, with advancements in electrical and optical tuning technologies, we anticipate\nthe realization of novel physical phenomena, such as harmonic generation. At that time, we will\nfurther explore harmonic superposition states and entanglement. It is worth noting that we have\nthe capability to perform full-wave modeling of time-varying systems and can achieve precise\nsolutions, with relevant work available for reference [R1]. Theoretically, we can accomplish\nfull-wave modeling and precise solving for any time-varying system.\n[R1] L. Chen et al., “Accurate Modeling of Time-Varying Lumped Elements in Space-Time\nMetasurfaces,” in IEEE Transactions on Antennas and Propagation, doi:\n10.1109/TAP.2025.3541920.\nAction Taken: In accordance with your comments, we provided a detailed supplementary\nexplanation regarding to the full-wave modeling in the revised manuscript to avoid any\npotential misunderstandings among readers. Additionally, we have included a discussion on the\nprospects of harmonic exploration. The specific modifications are as follows:\n[Introduction]\n… All numerical simulations were conducted based on the fundamental frequency, without\nconsidering the influence of other harmonic frequencies. …\n[Discussion]\n… In the future, with the realization of electrical and optical modulations, novel physical\nP\nA\nG\nE\nphenomena (e.g. harmonic generation) are anticipated. We will further explore superposition\nand nonseparable states of harmonic frequencies generated from high-speed time modulations\nto break through the current limitations of the fundamental frequency. …\n[Simulations]\n… In the mechanical modulation approach employed here, the control speed is much lower than\nthe EM wave propagation speed. Thus, this scenario can be treated as a quasi-static\nelectromagnetic problem. Consequently, in the numerical simulations, both superposition and\nnonseparable states of the quantum-inspired bits synthesized in the time dimension were treated\nas static, eliminating the need for time-varying modeling. …\nComment 1.5: How the authors want to fabricate this? (it seems very complicated and several\npractical maters need to be addressed)\nResponse: Thank you for this valuable question. In response to your concern regarding to the\ncomplexity of fabrication process, we remark that the implementation of quantum-inspired bits\nrequires dual-dimensional control of the system. Hence independent manipulation of each layer\nof the circular dielectric is needed. This inevitably introduces the dimensions of forward-\nbackward stepping and rotational movement of the stepper motors. Consequently, we designed\na metasurface composed of six layers, where the additional second, fourth, and sixth dielectric\nsubstrates serve to facilitate angular repositioning and mitigate interference among different\ndielectrics. With this design, transitions between different states can be accomplished in five\nsub-time intervals. It should be noted that the motor itself is responsible only for the rotational\ncontrol, while the forward-backward stepping is achieved through an additional stepping\nsystem that we have introduced. Looking ahead, we plan to explore more efficient experimental\nmethods, potentially extending to electrically or optically controlled modulation for faster\nadjustments.\nAction Taken: In accordance with your insightful comment, we have included relevant\nexplanations in the main text and provided a more detailed account of the fabrication and\nexperimental strategies in the Supplementary Information. This elaborates on how the\nmetasurface achieves the mechanical control under this design.\n[Experimental demonstration of reconfigurable time-varying metasurfaces]\n… Furthermore, we provide a more detailed experimental strategy to achieve more flexible\ncontrol in the Supplementary Information.\n[Meta-atom design and metasurface fabrication]\nP\nA\nG\nE\n… We also provide a detailed fabrication approach and corresponding experimental strategy in\nthe Supplementary Information for further research and applications.\n[Section 16: Details of the fabricated samples and their modulation demonstrations]\nIn this section, we present a detailed experimental strategy aimed at realizing the concept of\nquantum-inspired bits. The implementation of this concept inevitably requires the introduction\nof two control dimensions: the spatial rotation dimension and the forward-backward stepping\ndimension. The introduction of forward-backward stepping dimension allows the three-layer\ncircular insulator to rotate independently, thereby providing greater flexibility and precision for\nthe operation of quantum-inspired bits.\nFig. S20. Details of the fabricated samples. a Photo of the 4×4 supercell, with the stepping\nmotor mounted on its rear side. b Photo of a single meta-atom, equipped with a control stepping\nmotor and control board. c Schematic diagram of the layered structure of a single meta-atom,\nconsisting of a total of six layers.\nTo this end, we designed and constructed a reconfigurable metasurface platform, as\nillustrated in Fig. S20. Fig. S20a displays a sample of 4×4 dimensions, which is intended for\nscalability to larger sizes. Figure S20b presents a photograph of a reconfigurable meta-atom\nequipped with a stepping motor (model: 20HS2806A4) and a control board. Notably, these\nmeta-atoms were manufactured by Shenzhen Qiangda Circuit Co., Ltd. using the traditional\nP\nA\nG\nE\nPCB fabrication techniques. Additionally, we sourced the necessary gears from an online\nretailer, Jingcai Hardware (www.taobao.com), to facilitate the assembly of the mechanical\nsystem.\nFigure S20c further illustrates the layered structural schematic of the reconfigurable meta-\natom. Building upon the original three-layer circular insulator, we improved the structure to\nencompass a six-layer design. The newly added second, fourth, and sixth layers serve as\ndielectric bases, ensuring that the meta-atoms do not interfere with each other during the\nforward and backward stepping of the motor, thus enhancing the system’s stability. Furthermore,\nthese dielectric bases provide the necessary reset buffer time for the motor, ensuring smooth\noperational adjustments.\nFig. S21. Schematic demonstration of meta-atom based mechanical modulation.\nWe elaborate on the operation principles of the meta-atom under this design in Fig. S21.\nThe initial state of the meta-atom is set to (𝜃0 𝜃0 𝜃0). Once a specific state is designated,\n1 2 3\nthe motor first rotates the first layer of the insulator to the specified angle 𝜃1, then retracts it to\n1\nthe second layer to align with the initial state 𝜃0 of the third layer. Following this, the third\n2\nlayer is also rotated to the set angle 𝜃1, while the fourth layer is reset to maintain consistency\n2\nwith the initial state 𝜃0 of the fifth layer; finally, the fifth layer of the insulator is rotated to\n3\nthe specified angle 𝜃1 as well. Through this series of operations, we successfully modulate the\n3\nsystem from the initial state (𝜃0 𝜃0 𝜃0) to state-1 (𝜃1 𝜃1 𝜃1). Subsequently, state-1\n1 2 3 1 2 3\n(𝜃1 𝜃1 𝜃1) can transition to state-2 (𝜃2 𝜃2 𝜃2) by converting the retraction movement\n1 2 3 1 2 3\ninto a forward movement. It is important to note that the transition process between adjacent\nP\nA\nG\nE\nstates requires a buffer modulation time of five-time intervals to ensure system stability and\noperational precision.\nTherefore, future research will aim to explore additional feasible experimental\nmeasurement methods and consider extending this technology to faster control methods such\nas electrical and optical tuning. This will open new possibilities for applications in analog\nquantum computing and analog quantum communication.\nComment 1.6: Not all relevant references have been addressed.\nResponse and Action Taken: Thank you very much for your valuable suggestion. We\nrecognize that there were omissions in our references. In response, we have supplemented and\nrefined the relevant references in the revised manuscript. This modification will help enhance\nthe overall quality and academic rigor of the article.\n[Introduction]\n…rely on quantum bits (qubits)38-41 …… quantum metasurfaces45-54 …\n[40] Carrera Vazquez, A. et al. Combining quantum processors with real-time classical\ncommunication. Nature 636, 75–79 (2024).\n[41] Jäger, J. & Krems, R.V. Universal expressiveness of variational quantum classifiers and\nquantum kernels for support vector machines. Nat Commun 14, 576 (2023).\n[53] Wu, P. et al. Dynamic beam steering with all-dielectric electro-optic III–V multiple-\nquantum-well metasurfaces. Nat Commun 10, 3654 (2019).\n[54] Bekenstein, R. et al. Quantum metasurfaces with atom arrays. Nat. Phys. 16, 676–681\n(2020).\n[Superposition states in reconfigurable time-varying metasurfaces]\n… superposition57 and entanglement58,59 …\n[57] Zakka-Bajjani, E. et al. Quantum superposition of a single microwave photon in two\ndifferent ‘colour’ states. Nature Phys 7, 599–603 (2011).\n[58] Lin, Y. et al. Quantum entanglement between an atom and a molecule. Nature 581, 273–\n277 (2020).\n[59] Cai, W. et al. Protecting entanglement between logical qubits via quantum error\ncorrection. Nat. Phys. 20, 1022–1026 (2024).\n[Nonseparable states in reconfigurable time-varying metasurfaces]\n… To characterize the space-polarization nonseparable states60-62 …\n[61] Wang, R. et al. Single-antenna super-resolution positioning with nonseparable toroidal\npulses. Commun Phys 7, 356 (2024).\n[62] Wang, R. et al. Hybrid electromagnetic toroidal vortices. Sci. Adv. 11, eads4797 (2025).\nP\nA\nG\nE\nREVIEWER #2\nWe would like to thank Reviewer #2 for the positive comment regarding to our manuscript. In\nparticular, the reviewer states that “In my opinion, this work is impressive and I believe it makes\nsignificant contributions to the fields of information science, quantum physics, and material\nscience. Of course, one of the most immediate applications can be real-time arbitrary\npolarization conversion. The manuscript is also well-written and logically organized.\nIn summary, I consider this work to be valuable and recommend it for publication in Nature\nCommunications.” In addition, the reviewer provides a suggestion on how to improve our\nmanuscript. We thank the reviewer for the positive feedback on our manuscript and do\nappreciate the suggestion. The responses to the reviewer’s suggestions and the changes we have\nmade in response to the comment are outlined below.\nComment 2.1: Finally, I am curious about the response time of the system, and it would be great if the\nauthor could give more details.\nResponse: Thank you for your insightful question. It is important to clarify that the focus of\nthis work is on the conceptual proposal, which is why we employed a relatively simple\nmechanical modulation approach to validate our research platform. Currently, this method does\nresult in a slower response time for the system, primarily constrained by the maximum\nrotational speed of the motor, leading to a response time in the millisecond range. Additionally,\nwhen exploring superposition states and non-separable states, we concentrated primarily on the\nphenomena occurring at the fundamental frequency, allowing us to consider the system’s\nresponse time as negligible in terms of its impact on electromagnetic properties. In the future,\nwe plan to expand this platform to incorporate faster modulation techniques, such as electrical\nand optical controls, to facilitate the investigation of new physical phenomena and meet more\ncomplex application requirements.\nAction Taken: In response to your suggestion, we have provided a detailed explanation of\nthe system’s response time in the revised manuscript and noted that its impact on the current\nsystem’s electromagnetic characteristics can be disregarded. We have also outlined the future\nresearch directions. These modifications have enhanced the overall quality of our manuscript.\n[Reconfigurable time-varying metasurface]\n… It is important to emphasize that both the time interval and the system’s response time remain\non the order of milliseconds. …\n[Superposition states in reconfigurable time-varying metasurfaces]\nP\nA\nG\nE\nFig. 3 | … c,d,g,h The numerical simulations and theoretical predictions of the final polarization\nstates of the reflected wave under RCP and LCP incidences, taking into account the variations\nacross two distinct dimensional modulations. Since only the superposition state at the\nfundamental frequency is considered without involving the harmonics, the impact of the\nmechanical rotation speed on the two modulations is negligible. …\n[Experimental demonstration of reconfigurable time-varying metasurfaces]\n… It should be noted that while our reconfigurable time-varying metasurface demonstrates\neffectiveness based on a mechanical modulation approach, the modulation speed is inherently\ndependent on the performance of the motors used (i.e., on the millisecond scale). In practical\napplications, as the complexity of the applications increases, we may not be limited to the\nsuperposition states or nonseparable states at a single frequency, leading to a heightened\ndemand for increased modulation speeds. Therefore, we aim to extend this approach to\nelectrically or optically controlled high-speed modulation methods, although this may be\naccompanied by increased energy consumption. …\n[Discussion]\n… It should be noted that both investigations of the superposition and nonseparable states at\nthe fundamental frequency do not take into account the effects of harmonics, which implies that\nthe rotational speed of each meta-atom has a negligible impact on the modulation. …\n… However, the mechanical modulation employed in the current reconfigurable time-varying\nmetasurface platform is entirely dependent on the performance of the motors, which limits its\noperational processing speed. As the demands for practical applications increase, the proposed\nreconfigurable time-varying metasurface should be further expanded through electrical and\noptical control methods, enabling faster modulation speeds and more complex system functions,\nsuch as analog simulations of quantum gates and quantum circuits within classical EM systems.\nIn the future, with the realization of electrical and optical modulations, novel physical\nphenomena (e.g. harmonic generation) are anticipated. We will further explore superposition\nand nonseparable states of harmonic frequencies generated from high-speed time modulations\nto break through the current limitations of the fundamental frequency. …\n[Section 15: Details of the stepping motor]\nP\nA\nG\nE\nTable S1. Electrical performance. These stepping motors were brought from a\ncommercial company named Wuxi Stepping Automatic Control Technology Co., Ltd. in\nWuxi, China.\nStep angle 1.8 °⁄𝑺𝒕𝒆𝒑\nRated voltage 1.92 𝑽\nCurrent 0.6 𝑨⁄𝑷𝒉𝒂𝒔𝒆\nResistance 3.2 𝛀⁄𝑺𝒕𝒆𝒑\nInductance 0.9 𝒎𝑯⁄𝑺𝒕𝒆𝒑\nHolding torque 1.4 𝑵.𝒄𝒎\nDetent torque 0.2 𝑵.𝒄𝒎\nRotor inertia 2.5 𝒈.𝒄𝒎𝟐\nMotor length 28 𝒎𝒎\nLead wire 4 𝑵𝑶\nMotor weight 50 𝒈\nFig. S19. Photo and detailed geometric parameters (mm) of the adopted stepping motor.\nThe stepping motor used in this work is illustrated in Fig. S19, with the detailed electrical\nperformance provided in Table S1. It is noteworthy that the rotational speed of this stepping\nmotor is approximately 4000 revolutions per minute, resulting in a system response time on the\norder of milliseconds.\nP\nA\nG\nE\nAuthors’ Responses\nREVIEWER #3\nWe sincerely appreciate Reviewer #3 (R3) for the time and effort invested in reviewing our\nmanuscript and offering insightful comments and thoughtful suggestions. In particular, R3\nstates that “The paper presents designs of reconfigurable metasurfaces for arbitrary\npolarization control. The designs are at microwave frequencies and are based on three-layer\ncomposite meta-atoms. The polarization control is achieved by varying the orientation angles\nbetween different layers of each meta-atom and the orientation angle of the entire meta-atom.\nThis functionality is achieved mechanically by using motors, in contrast to other works that\nrely on electric tuning based on varactors of pin diodes. The design is interesting from an\nengineering point of view, since in principle it can realize any polarization state for the\nreflected wave. ... Overall, the paper presents an interesting engineering design of\nreconfigurable metasurfaces.” These comments and suggestions are extremely valuable to\nenhance the quality of our manuscript. Following R3’s constructive feedback, we have\ncarefully revised the paper to improve its clarity and comprehensibility. The authors thank R3\nfor the invaluable comments and constructive suggestions, which have greatly contributed to\nsignificantly improving the quality of this paper.\nComment 3.1: The design is interesting from an engineering point of view, since in principle it\ncan realize any polarization state for the reflected wave. At the same time, the literature on\npolarization conversion metasurfaces in abundant in engineering journals. It is unclear in\nwhat aspects the present work is different from such prior work. My feeling is that the\npresented approach truly offers unique control on polarization, but without a detailed\ncomparison with other works, it is difficult to make a definite statement on this aspect. On a\nrelated issue, the Authors should provide a broader coverage of relevant papers from IEEE or\nother engineering journals, since this is the literature against which their work needs to be\ncompared.\nResponse: Thank you for your insightful question. First, we would like to reiterate the\ninnovations and contributions of our work. Our primary innovation is proposing the concept\nof “quantum-inspired bit,” which is at the forefront of current research on quantum-inspired\nmetasurfaces. Additionally, our contribution is developing a metasurface-based physical\nplatform that can experimentally implement this novel and important concept.\nIt is important to emphasize that the main idea of this paper extends beyond achieving\narbitrary polarization states for the reflected wave. A significant contribution lies in the\nexperimental realization of output polarization coverage over the entire Poincaré sphere,\nthereby implementing our novel \"quantum-inspired bit\" concept—an achievement unattained\nP\nA\nG\nE\nby prior works. More specifically, the implementation of our proposed “quantum-inspired bit”\nnecessitates the simultaneous fulfillment of the following key conditions:\n1) All output polarization states should be generated at the same frequency;\n2) All output polarization states should be produced from the same input polarization\nstate;\n3) The metasurface should be dynamically tunable, enabling the realization of this\nquantum-inspired bit concept through temporal accumulation;\n4) The output polarization states must exhibit full coverage of the Poincaré sphere to\nrealize the proposed \"quantum-inspired bit\" which functionally emulates the\nrepresentation of quantum bits on the Bloch sphere.\nIn response to your suggestion regarding comparisons to previous polarization\nconversion works, we conducted a thorough literature review. While there are a variety of\nmodulation methods reported in the literature, to date, none have been able to simultaneously\nmeet all four key conditions for realizing the quantum-inspired bit concept we propose. For\ninstance, rapid electro-tuning methods, which are highly regarded for their swift response\ntimes, primarily rely on PIN diodes and varactor diodes. However, PIN diodes are limited to\ntwo switching states, and even when multiple diodes are integrated into a single unit, the\nachievable polarization states remain constrained. This limitation prevents existing research\nfrom realizing the proposed \"quantum-inspired bit\" concept. Although varactor diodes support\ncontinuous tuning, they generally can only achieve a limited number of combinations when\nconverting an arbitrary single polarization state into a polarization output combination.\nConsequently, they do not fulfill the abovementioned four key conditions. In this work, we\ndevelop a reconfigurable time-varying metasurface that satisfies all four key requirements,\nwhich are essential for implementing our proposed \"quantum-inspired bit\" concept and cannot\nachieved by previous works.\nAction Taken: To response your good comments, we have included a detailed comparison of\nour work with other works in the revised manuscript. This aims to demonstrate that existing\nworks is unable to realize our proposed “quantum-inspired bit” concept, thereby further\nhighlighting the novelty of our platform.\n[Supplementary Section 17: Comparison with other works]\nHere, we compare our work with other studies on polarization conversion metasurfaces4-18,\nfocusing on the four conditions that are necessary to realize the quantum-inspired bits, as well\nas the feasibility to achieve the “quantum-inspired bit” concept.\nTo truly realize the concept of “quantum-inspired bit,” several key conditions need to be\nsatisfied:\n1) all output polarization states should be generated under the same polarization excitation;\n2) all output polarization states should be produced at the same frequency point;\n3) the introduction of a temporal dimension is necessary to ensure the overall platform is\nP\nA\nG\nE\ntunable, as the realization of quantum-inspired bits relies on the accumulation of time;\n4) it is essential to achieve arbitrary polarization output that covers the entire Poincaré\nsphere, which is similar to how quantum bits characterize the Bloch sphere.\nSupplementary Table 2 clearly indicates that the current electrically tunable metasurfaces\nprimarily depend on PIN diodes and varactor diodes for polarization conversion. Firstly, the\nPIN diodes exhibit only two switching states; even when multiple diodes are integrated into a\nsingle unit, the achievable output polarization states remain limited. The varactor diodes do\noffer continuous tuning capabilities, but the existing reports indicate that they are unable to\ncover the entire Poincaré sphere6,15. Therefore, the researches on electrically controlled\nmetasurfaces face challenges in realizing the “quantum-inspired bit” concept4-15,17.\nIn addition, the other modulation methods such as liquid crystals tend to have slower\ntuning speeds and also do not fulfill our new concept16. The current research on arbitrary\npolarization output primarily relies on non-tunable metasurfaces by altering geometric\nparameters18. However, due to the lack of a temporal dimension, this approach does not\nsatisfy the third condition and therefore cannot meet the requirements for the proposed\n“quantum-inspired bit” concept.\nOur platform provides a feasible solution to address these requirements. However, it is\nimportant to note that we do not deny the potentials for electrically tunable or optically\ntunable methods to eventually realize our concept; rather, we acknowledge that, based on the\nexisting reports, this has not yet been achieved. We believe that exploring faster control\nmethods for polarization output based on electrical or optical modulation is highly significant,\nas it could enable dynamic adjustments of the sphere’s position while covering the entire\nPoincaré sphere, which is certainly a promising avenue for future research.\n[4] Li, W., Guo, H., Wang, X., Yang, G.M. & Jin, Y.Q. A 2-bit Reconfigurable Metasurface\nWith Real-Time Control for Deflection, Diffusion, and Polarization. IEEE Trans.\nAntennas Propag. 72, 1521-1531 (2024).\n[5] Yang, H., Wang, S.C., Li, P., He, Y. & Zhang, Y.J. A Broadband Multifunctional\nReconfigurable Polarization Conversion Metasurface. IEEE Trans. Antennas Propag. 71,\n5759-5767 (2023).\n[6] Gao, X., et al. A Reconfigurable Broadband Polarization Converter Based on an Active\nMetasurface. IEEE Trans. Antennas Propag. 66, 6086-6095 (2018).\n[7] Li, W., et al. A Reconfigurable Polarization Converter Using Active Metasurface and Its\nApplication in Horn Antenna. IEEE Trans. Antennas Propag. 64, 5281-5290 (2016).\n[8] Yang, H., et al. A Reflection–Transmission Multifunctional Polarization Conversion\nMetasurface. IEEE Trans. Antennas Propag. 72, 5099-5109 (2024).\n[9] Khan, H.A., Zhang, J., Luo, S. & Wang, Y. A Single-Layer Checkerboard Metasurface\nBased on Reconfigurable Polarization Converter for Dual-Mode RCS Reduction. IEEE\nAntennas Wirel. Propag. Lett. 24, 2029-2033 (2025).\nP\nA\nG\nE\n[10] Li, Y., Cao, Q. & Wang, Y. A Wideband Multifunctional Multilayer Switchable Linear\nPolarization Metasurface. IEEE Antennas Wirel. Propag. Lett. 17, 1314-1318 (2018).\n[11] Pramanik, S., et al. Active Metasurface-Based Reconfigurable Polarization Converter\nWith Multiple and Simultaneous Functionalities. IEEE Antennas Wirel. Propag. Lett. 22,\n522-526 (2023).\n[12] Liu, D.Q., et al. An Active Metasurface for Dynamic Polarization Conversion and\nIndependent Amplitude Control. IEEE Trans. Antennas Propag., 1-1 (2025).\n[13] Liu, W., et al. Broadband Polarization-Reconfigurable Converter Using Active\nMetasurfaces. IEEE Trans. Antennas Propag. 71, 3725-3730 (2023).\n[14] Guo, Q., Hao, F., Qu, M., Su, J. & Li, Z. Multiband Multifunctional Polarization\nConverter Based on Reconfigurable Metasurface. IEEE Antennas Wirel. Propag. Lett. 23,\n1241-1245 (2024).\n[15] Yang, X., Wen, E., Bharadia, D. & Sievenpiper, D.F. Multifunctional Metasurface:\nSimultaneous Beam Steering, Polarization Conversion, and Phase Offset. IEEE Trans.\nAntennas Propag. 72, 4589-4593 (2024).\n[16] Deng, G., et al. Reconfigurable Broadband Transmissive-Type Polarization Converter\nBased on Liquid Crystal Metasurfaces. IEEE Antennas Wirel. Propag. Lett. 24,\n2327-2331 (2025).\n[17] Zhou, H., Yu, X., Wang, P., Wang, Y. & Yan, Z. Wideband Linear-to-Multi-Polarization\nConverter Based on Active Metasurface. IEEE Trans. Antennas Propag. 71, 5246-5255\n(2023).\n[18] Liu, T., et al. Arbitrary polarization conversion and phase control using full- parameter\nAA-phase metasurface. in 2024 IEEE 7th International Conference on Electronic\nInformation and Communication Technology (ICEICT) 1169-1171 (2024).\nSupplementary Table 2. Comparison of our work with other works on\npolarization-converting metasurfaces\nTunable Oblique Cond. Cond. Cond. Cond. Feasibility of\nRef.\ndevice angle 1 2 3 4 quantum-inspired bits\n[4] PIN -     No\n[5] PIN -     No\n[6] Varactor -     No\n[7] PIN -     No\n[8] PIN 50°     No\nP\nA\nG\nE\n[9] PIN 30°     No\n[10] PIN 20°     No\n[11] PIN 10°     No\n[12] PA 40°     No\n[13] PIN 30°     No\n[14] PIN -     No\n[15] Varactor -     No\nLiquid\n[16] -     No\ncrystal\n[17] PIN -     No\n[18] - -     No\nOur Electric\n45°     Yes\nwork motor\n[Experimental demonstration of reconfigurable time-varying metasurfaces]\n… In fact, the existing literature has reported various faster modulation methods, such as\nelectrical or optical tuning approaches. However, realizing the concept of the\nquantum-inspired bits requires to meet four necessary conditions, which cannot be achieved\nby the current reports. Therefore, in this initial attempt, we just firstly realize the functionality.\nFor a more detailed comparison between this work and the related studies, please refer to\nSupplementary Section 17. …\nComment 3.2: In their analysis, the Authors make heavy use of quantum terminology.\nAlthough drawing analogies with other fields is interesting, over-reliance on quantum\nterminology is unnecessary here and possibly confusing. The structures presented in the paper\nare completely classical and can be fully described through classical EM theory. What the\nAuthors call superposition states are elliptically polarized waves, which are well known that\ncan be decomposed to circularly polarized waves of opposite handedness. A quantum\ndescription would make sense if the structures were used in quantum information processing,\nbut this is not the case here.\nResponse: Thank you very much for your valuable suggestions and insightful questions. We\nrecognize that the background information provided in the original manuscript may not have\nP\nA\nG\nE\nbeen sufficiently clear, which could have led to your confusion.\nOur research primarily focuses on mimicking specific quantum effects within a classical\nframework, particularly using quantum bits (qubits) as the core subject of study. To effectively\nmimic the characteristics of qubits, we introduced a new concept termed “quantum-inspired\nbit,” aimed at modeling superposition and entangled states. This concept represents a\nsignificant innovation in our research, as our primary objective is not solely to achieve\npolarization conversion. In the field of quantum information, qubits serve as the fundamental\nunits of information processing; however, their practical applications face numerous\nchallenges, including difficulties in preparation, stringent experimental conditions, complex\noperations, and susceptibility to collapse. Thus, we aim to achieve a robust bit similar to\nqubits within a classical framework, namely the quantum-inspired bit.\nFurthermore, our research is inspired by the “information metasurface” concept first\nproposed in 2014, initially aimed at facilitating digital encoding in metasurfaces and\nsubsequently extended to the field of information metasurfaces. Although the basic processing\nunit of information metasurfaces remains classical bits, the limitations of classical bit capacity\nhave prompted us to explore the potential of quantum-inspired bits for achieving higher\ninformation capacity. It is based on this dual consideration that we propose the new concept of\nquantum-inspired bits in our study.\nAdditionally, we wish to highlight a currently prominent and cutting-edge area:\n“quantum-inspired metasurfaces” [R1]. This field represents the forefront of research, where\nmetasurfaces operate in the classical domain yet can mimic specific quantum effects—such as\nutilizing non-separable states to mimic quantum entanglement [R2], mimicking quantum\ntunneling effects [R3][R4], and constructing time crystals [R5]. These metasurfaces are not\nintended for quantum information processing but aim to achieve efficient information\nprocessing within classical systems, drawing inspiration from quantum effects.\n[R1] Ren, Z., et al. Terahertz Metamaterials Inspired by Quantum Phenomena. Research 8,\n0597 (2025)\n[R2] Y. Shen, C. Rosales-Guzmán, Nonseparable States of Light: From Quantum to\nClassical. Laser & Photonics Reviews 16, 2100533 (2022).\n[R3] Xue Jiang et al., Direct observation of Klein tunneling in phononic crystals. Science 370,\n1447-1450 (2020).\n[R4] Lee, Daehun et al. Klein tunneling of gigahertz elastic waves in nanoelectromechanical\nmetamaterials. Device 2, 100474 (2024).\n[R5] Liu, T., Ou, JY., MacDonald, K.F. et al. Photonic metamaterial analogue of a\ncontinuous time crystal. Nat. Phys. 19, 986–991 (2023).\nAction Taken: In response to your feedback, we have revised the introduction of the\nmanuscript to provide a more detailed explanation of the relationship between our research\nstructure and quantum information processing, and to clarify that our work falls within the\nrealm of quantum-inspired metasurfaces, thereby avoiding potential misunderstandings.\nP\nA\nG\nE\n[Introduction]\nIn recent years, the continuous advancement of quantum mechanics1-3 has drawn increasing\nattention to the field of quantum information science. As a revolutionary discipline bridging\nquantum physics and information science, quantum information science4-6 is poised to\ntransform scientific and technological paradigms due to its immense application potential and\nadvantages. Specifically, quantum communication7-10 ensures the security of information\nbased on the principles of quantum physics, while quantum computing11-14 offers\ncomputational capabilities that surpass those of classical computers, driving revolutions in\nmaterials science, chemistry, and biomedicine. Furthermore, advancements in quantum\nsensing15-18 and measurement19-21 technologies have significantly enhanced the performance\nof traditional sensing and measurement systems.\nThe allure of quantum information science has not only catalyzed the development of\nquantum metasurfaces22-25 but also fostered the flourishing of quantum optics26,27.\nMetasurfaces28-32 are planar artificial structures composed of subwavelength unit cells,\ndesigned in a periodic or non-periodic arrangement. Although initial metasurfaces lacked the\nability to modify electromagnetic (EM) responses post-fabrication33,34, which limited their\npractical applications, researchers have proposed the concept of reconfigurable metasurfaces\nas a solution to this limitation35-38. In contrast to traditional classical metasurfaces,\nquantum metasurfaces represent a significant advancement, providing a critical research platform for\ngenerating, manipulating, and detecting non-classical EM waves. However, the stringent\nconditions required for the fabrication, manipulation, and testing of quantum metasurfaces\ncurrently pose significant challenges to their practicality.\nConcurrently, the concept of digital coding metasurfaces39 has evolved into that of\ninformation metasurfaces40-48, bridging the realms of classical physics and information\nscience. While the basic information processing units of information metasurfaces are based\non classical bits, which offer stability, ease of storage and transmission, and straightforward\noperation, they exhibit limitations in scalability and parallel processing capabilities. In\ncontrast, quantum bits49-51 present unprecedented advantages in computational speed and\nparallelism, enabling the resolution of complex problems that classical bits cannot tackle.\nNevertheless, quantum bits are often unstable, making storage and transmission challenging,\nand they are highly sensitive to environmental disturbances, necessitating complex error\ncorrection techniques. Consequently, implementing their advantages within classical systems\nremains a formidable challenge. This underscores the need for a feasible physical platform\ncapable of mimicking the characteristics of quantum bits while achieving a high degree of\ncomputational freedom in stable classical EM systems. The concept of quantum-inspired\nmetamaterials52,53 provides a promising avenue for addressing this challenge.\nP\nA\nG\nE\nComment 3.3: As other reviewers have pointed out, one challenge of the proposed approach\nis its reliance on mechanical motors. In addition to their inherently low speed, this approach\nis probably difficult to scale up in frequency and size. The Authors have recognized this\nproblem, but they have not provided any information on possible solutions. Implementing a\ncontinuous rotation between the layers of meta-atoms by using electronic elements would\nprobably be difficult. In that regard, it seems that the proposed approach is limited to low\nfrequencies and low modulation speeds.\nResponse: Thank you very much for your insightful question. We acknowledge that the\ncurrent dependence on mechanical drive limits the operational frequency range to the\nmicrowave band, which presents challenges for further expansion. However, regarding size,\nour mechanical platform employs a modular design that theoretically allows for extension to\nlarger dimensions. At present, this platform is indeed suitable for low-frequency applications\nand low modulation rate scenarios.\nFirst, we would like to clarify that, although we are currently unable to increase the\noperational frequency, the microwave band itself holds significant practical value, particularly\nin communication and sensing applications. Furthermore, we must emphasize that the core\ninnovation of this study lies in the introduction of the concept of “quantum-inspired bit.” We\nhave provided theoretical evidence (as shown in Figure R1) demonstrating the analogy\nbetween quantum-inspired bits and qubits. We have proposed a new theoretical framework for\nboth the superposition state and nonseparable state of quantum-inspired bits. Specifically, the\nmathematical representation of the superposition state can be found in Supplementary\nSection 1: “Mathematical representation of the superposition state in reconfigurable\ntime-varying metasurface” and Supplementary Section 13: “Theoretical model based on\nthe transformation of the Jones matrix.” For the nonseparable state, its mathematical\nrepresentation is detailed in Supplementary Section 2: “Theoretical framework for the\nnonseparable state in reconfigurable time-varying metasurface.”\nIn addition, we have conducted extensive literature research, and to date, existing reports\nhave not realized this new concept, while our platform has proven to be feasible, with no\nmore efficient or faster platforms identified. Although our platform is primarily used to\nvalidate conceptual feasibility, this does not detract from the originality of our work, as noted\nin Comment 3.1.\nP\nA\nG\nE\nFig. R1 | The quantum-inspired bit based on PB-phase meta-atom to emulate the\nquantum bit in terms of the mathematical and geometric representations.\nRegarding the solution you mentioned, while we currently do not have the capability for\nelectrically controlled functions, we appreciate your question, as it provides us with important\ninsights. We recognize that if we can independently control two dimensions under the same\npolarization incident conditions, it would allow for arbitrary polarization output. When the\nstructure is symmetrical in both the x and y directions, we can integrate independently tunable\ncomponents to modulate the x-polarized and y-polarized incident waves separately, adjusting\ntheir amplitude and phase. If the amplitude control in both directions is consistent while the\nphase is independently modulated, it can output circularly polarized or any linearly polarized\nwaves; conversely, if the amplitude modulation in both directions is inconsistent while\nallowing for phase-independent continuous modulation, it can output any elliptical polarized\nwave. Therefore, in the future, if we can design such a unit structure capable of modulating in\nboth dimensions (amplitude and phase), it may be possible to realize the electrically\ncontrolled concept of “quantum-inspired bit.” Although this concept is still in the theoretical\nstage, we believe that such a platform holds potential for feasibility.\nAction Taken: In response to your concerns, we have revised the manuscript to include this\npotential solution.\n[Discussion]\n… In this context, it is essential to achieve synchronous controls in two dimensions for\nindependently modulating the two coordinate dimensions of the Poincaré sphere. At the same\ntime, any single circularly polarized input wave can be decomposed into two orthogonal\npolarizations, x and y. By introducing a method that can independently modulate the\namplitudes and phases of the incident x and y polarized waves, one will achieve the\ngeneration of EM waves with arbitrary polarization states. Leveraging this independent\nP\nA\nG\nE\ncontrol capability, we anticipate the potential to generate any desired output polarization\nstates, thereby realizing the electrically tunable quantum-inspired bits. …\nComment 3.4: The Authors claim that mechanical reconfigurability is more energy-effective\nthan electrical reconfigurability. I am skeptical about this. For example, varactors can\nchange their capacitance with negligible energy consumption. More generally, it seems\ndoubtful that electric motors would consume less energy than electronic components with a\nsize that is orders of magnitude smaller than motors.\nResponse: Thank you very much for raising this important question. We apologize for the\ninaccuracies in our original manuscript regarding energy consumption. In the introduction,\nour intention was to convey that, in many cases, when reconfigurable metasurfaces are\nrequired to perform continuous tasks, such as during communication, mechanical\nmetasurfaces need to drive motors, which can lead to higher energy consumption. However, it\nis important to note that during the execution of communication tasks, mechanical\nmetasurfaces can cease power supply while still maintaining functionality. In contrast,\nelectrically reconfigurable metasurfaces require continuous power supply during this period;\nonce the power supply is interrupted, they can no longer perform their tasks. This\ncharacteristic contributes to the excellent non-volatility of mechanical metasurfaces, allowing\nthem to fulfill their designated functions even in the absence of power, which is something\nelectrically driven metasurfaces cannot achieve.\nWe have provided specific explanations in Figure R2, and relevant literature [R6][R7]\nalso addresses this topic. However, we acknowledge that the scenario presented in our\nmanuscript is somewhat unique; to realize the concept of quantum-inspired bits that we\nproposed, continuous power supply is indeed necessary.\n[R6] Quan, X., et al. Mechanically reprogrammable Pancharatnam–Berry metasurface for\nmicrowaves. Adv. Photonics 4, 016002 (2022).\n[R7] Fan, Z., et al. Homeostatic neuro-metasurfaces for dynamic wireless channel\nmanagement. Science Advances 8, eabn7905 (2022).\nP\nA\nG\nE\nFig.R2 | Comparison of power consumption between electrical modulation and\nmechanical modulation.\nAction Taken: In response to your feedback and to prevent similar confusion for other\nreaders, we have removed all potentially misleading statements related to energy consumption\nand have made detailed revisions to the introduction.\nComment 3.5: Overall, the paper presents an interesting engineering design of\nreconfigurable metasurfaces. However, it needs to be placed better in the context of other\nreconfigurable metasurfaces to assess the merits of the design. It is especially important to\nprovide quantitative comparisons with other works in terms of tuning resolution, loss, speed,\nor other relevant metrics. Finally, the paper seems to be more suitable for a more technical\njournal rather than Nature Communications.\nResponse and Action Taken: Thank you very much for your valuable comments and\nfeedback on our manuscript. We sincerely apologize for any confusion that the original\nsubmission may have caused. Indeed, our emphasis on the characteristics of reconfigurable\nmetasurfaces in the introduction may have overshadowed the core background of our\nwork—quantum-inspired metasurfaces—leading you to perceive our paper as primarily\nfocused on design. In light of this, we have comprehensively rewritten the introduction to\nemphasize that the main focus of our research lies in physical sciences, particularly in the\nfield of quantum information. We also highlight its contributions to engineering, aiming to\nattract interest from multiple disciplines.\nWe would like to clarify once again, as mentioned in our previous response, that our\ncentral innovation lies in proposing a novel concept of quantum-inspired bits within a\nclassical framework, along with the development of a platform intended for proof-of-principle\nvalidation. This platform is not the primary innovation of our work; rather, it supports the\nvalidity of our theoretical contributions. Quantum-inspired metasurfaces have long been a\nfrontier topic in scientific research, and our work fundamentally represents an innovation in\nP\nA\nG\nE\nthe field of physical sciences, rather than merely an engineering accomplishment. The concept\nof quantum-inspired bits holds significant appeal for physical sciences, while the innovative\nplatform we propose is also likely to attract interest from engineering researchers. Therefore,\nwe firmly believe that our work will engage scholars from diverse fields such as physical,\napplied, and engineering sciences.\nThis perspective has also been acknowledged by other reviewers, as they noted: “The\npaper presents a classical/quantum qbits controlled by time modulation metasurfaces. … In\nthe submitted manuscript “Superposition and nonseparable states in reconfigurable\ntime-varying metasurfaces”, Long Chen et al. have reported on the realization of the analog\nof quantum bits (qubits) in classical systems, which referred to “intermediate states”\nbetween the classical and quantum bits in the manuscript. To explore the superposition and\nnonseparability of the intermediate states, the authors have designed a mechanically\ncontrolled time-varying metasurface. … In my opinion, this work is impressive and I believe it\nmakes significant contributions to the fields of information science, quantum physics, and\nmaterial science. Of course, one of the most immediate applications can be real-time arbitrary\npolarization conversion. The manuscript is also well-written and logically\norganized. … In summary, I consider this work to be valuable and recommend it for\npublication in Nature Communications.”.\nAs a high-quality journal that attracts researchers from various fields, Nature\nCommunications is indeed a suitable venue for our research. To prevent potential\nmisunderstandings by future readers, we have enhanced the significance of our work in the\nrevised manuscript.\n[Introduction]\n… We believe that the introduction of quantum-inspired bit and the realization of\nreconfigurable array platform will advance the developments in various fields, including\nquantum physics, information science, and metamaterials.\n[Discussion]\n… With the achievement of faster quantum-inspired bits, the proposed methodology may\nsignificantly advance both quantum and classical domains simultaneously. In the quantum\nrealm, the related research could provide new perspectives for quantum physics, exploring\npotentially new physical phenomena. In the classical realm, it will promote the realization of\nhigh-speed and high-capacity information platforms, facilitating the advancements in\nmetamaterials and information science, thus contributing to both new theories and practical\napplications.\nP\nA\nG\nE\nAuthors’ Responses\nTO REVIEWER #3\nWe sincerely thank you for the time and effort invested in reviewing our manuscript and offering\nthe insightful comments and thoughtful suggestions. In particular, you stated that “The Authors\nprovided a detailed response to my comments, which is much appreciated. They performed a\nthorough comparison with other works on tunable metasurfaces, which makes the benefits of\ntheir design clearer. …. Aside the practical concerns related to the mechanical parts of the\ndesign, I think this achievement is by itself very interesting and unique. One could envision that\nsomeday such metasurfaces could find applications in preparation of quantum states.” These\ncomments and suggestions are extremely valuable to enhance the quality of our manuscript.\nFollowing your constructive feedback, we carefully revised the paper to improve its clarity and\ncomprehensibility. Below are our point-to-point responses to your comments.\nComment 1:\nAs I mentioned in my original review, the main novelty of the paper is the presentation of\nmetasurface designs that can dynamically convert a polarization state to any other polarization\nstate. Aside the practical concerns related to the mechanical parts of the design, I think this\nachievement is by itself very interesting and unique. One could envision that someday such\nmetasurfaces could find applications in preparation of quantum states. However, this does not\nchange the fact that this is not the case with the metasurfaces in the paper, which are designed\nto generate classical elliptical polarization states. Even if the Authors prefer using the\n\"superposition\" and \"nonseparable\" terminology, I think at least the title should clearly reflect\nthe classical nature of the design.\nResponse and Action Taken:\nThank you very much for your valuable suggestions. Following your recommendation, we\nhave revised the title of the manuscript to “Quantum-inspired superposition and nonseparable\nstates of reconfigurable metasurfaces in classical systems” to more clearly reflect the classical\nnature of the design.\n[Title]\nQuantum-inspired superposition and nonseparable states of reconfigurable metasurfaces in\nclassical systems\nFurthermore, we have carefully revised the main text and supplementary materials to\nreplace the “superposition state” and “nonseparable state” by “analog superposition state” and\n“analog nonseparable state,” respectively. We have also clarified that these states are\n“quantum-inspired” states that are implemented in the classical system rather than a\nP\nA\nG\nE\nquantum system. More details of our revision can be found below:\n[Abstract]\n Here, analog superposition states and analog nonseparable states are theoretically ...\n To implement these two quantum-inspired states in classical systems, we have developed\na reconfigurable time-varying metasurface capable of synthesizing analog superposition\nstates across the temporal dimension and analog nonseparable states across spatial and\npolarization dimensions. Due to its unique features of analog superposition and analog\nnonseparability, ...\n[Introduction]\n We should clarify that the quantum-inspired states discussed here are implemented in a\nclassical system rather than in a quantum system.\n the mathematical and geometric representations of the analog superposition state ...\n describe the analog superposition state, ...\n the concept and mathematical framework of the analog superposition state to explore the\nanalog superposition behavior of the EM waves based on the reconfigurable metasurface\nin a classical system ...\n which is a crucial ability to implement the analog superposition state. We further\ndemonstrate an analog nonseparable state that mirrors ...\n realize the concept of quantum-inspired states. ...\n[Reconfigurable time-varying metasurface]\n the state of which can be mathematically expressed as an analog superposition state: ...\n To implement the aforementioned analog superposition state, …\n Additionally, the metasurface exhibits analog nonseparable state properties, ...\n Given that the analog superposition state corresponds to the ...\n In our case, the analog superposition of states is implemented in ...\n In principle, minimizing the time interval towards zero would yield an analogue of the qubit\nsuperposition state. More details of the theoretical derivations for the mathematical and\ngeometric representations of the analog superposition state in ...\n[Reconfigurable time-varying meta-atom]\n the proposed theory of analog superposition states in reconfigurable time-varying\nmetasurfaces ...\n In order to ensure the reliability and accuracy of the analog superposition state in ...\n the geometric representation of the analog superposition state on ...\n From an application perspective, the analog superposition states in ...\n Further details on the broadband validation of the analog superposition state are ...\n both mathematical and geometric representations of analog superposition states in ...\n[Analog superposition state of reconfigurable metasurfaces in classical systems]\nP\nA\nG\nE\n here we study the analog superposition state in ...\n manipulate the analog superposition state of the ...\n To realize the analog superposition state in ...\n This allows to construct the analog superposition states on ...\n It should be noted that the analog superposition states have been ...\n on the performance of the analog superposition states is ...\n[Analog nonseparable state of reconfigurable metasurfaces in classical systems]\n To characterize the analog nonseparable states of space-polarization60,61 in ...\n to demonstrate the analog nonseparable correlation ...\n we can establish an analog nonseparable state based on ...\n exhibit an analog nonseparable state between ...\n Hence, we validate that an analog nonseparable state between ...\n[Experimental demonstration of reconfigurable time-varying metasurfaces]\n metasurface is capable of characterizing the analog superposition state to yield an analogue\nof the qubit superposition state, we ...\n the mathematical and geometric representations for the analog superposition state in ...\n be limited to the analog superposition states or analog nonseparable states at ...\n[Discussion]\n facilitating the exploration of analog superposition states and analog nonseparable states.\nIt should be noted that both investigations of the analog superposition states and analog\nnonseparable states at ...\n both mathematical and geometric representations of the analog superposition state within ...\n crafted for the analog superposition state. ...\n the geometric representation of the analog superposition state can be ...\n explore the potential for an analog nonseparable state of space-polarization between ...\n a feasible physical platform to implement the analog superposition state. ...\n[Methods]\n both analog superposition states and analog nonseparable states of ...\n The analog superposition properties of the meta-atoms were ...\n investigate the analog nonseparable state in ...\n It should note that the analog nonseparable state simulation ...\n[Fig.1]\n which exhibits an analog nonseparable state of space-polarization between ...\n[Fig.3]\n Analog superposition state in ...\n Since only the analog superposition state at the ...\n[Fig.4]\nP\nA\nG\nE\n Analog nonseparable state of space-polarization between ...\n[Fig.5]\n Experimental verification of the analog superposition state in ...\n of the analog superposition state in reconfigurable ...\n[Supplementary Section 1: Mathematical representation of the analog superposition state\nin reconfigurable time-varying metasurface]\n a mathematical portrayal of the analog superposition state in ...\n the mathematical representations of the analog superposition state derived ...\n[Supplementary Section 2: Theoretical framework for the analog nonseparable state in\nreconfigurable time-varying metasurface]\n To characterize the analog nonseparable state in ...\n takes an analog nonseparable form representing ...\n[Supplementary Section 5: Experimental setup for verifying the analog superposition\ncharacteristics in reconfigurable time-varying metasurface]\n validations of all analog superposition properties within ...\n verifying analog superposition characteristic in ...\n[Supplementary Section 7: Impact of different polarizations and angles of incident wave\non analog superposition state in reconfigurable time-varying metasurface]\n and their analog superposition state, we ...\n the mathematical representation of the analog superposition state is ...\n[Supplementary Section 9: Fidelity of the analog superposition state in reconfigurable\ntime-varying metasurface]\n mathematical representation of the analog superposition state in reconfigurable ...\n[Supplementary Section 11: The influence of lattice geometries on the properties of meta-\natoms]\n can also achieve the analog superposition state, as ...\n higher precision in controlling the analog superposition state in ...\n[Supplementary Section 12: Broadband validation of the analog superposition state in\nreconfigurable time-varying metasurface]\n geometric representation of the analog superposition state in ...\n characterizing the analog superposition state’s geometric representation ...\nComment 2:\nAs I mentioned in my original review, the main novelty of the paper is the presentation of\nmetasurface designs that can dynamically convert a polarization state to any other polarization\nstate. Aside the practical concerns related to the mechanical parts of the design, I think this\nachievement is by itself very interesting and unique. One could envision that someday such\nmetasurfaces could find applications in preparation of quantum states. However, this does not\nchange the fact that this is not the case with the metasurfaces in the paper, which are designed\nto generate classical elliptical polarization states. Even if the Authors prefer using the\n\"superposition\" and \"nonseparable\" terminology, I think at least the title should clearly reflect\nthe classical nature of the design.\nResponse and Action Taken:\nWe appreciate your valuable feedback and sincerely apologize for any ambiguity arising\nfrom our initial discussion in the Introduction. In response to your suggestions, we have\nthoroughly revised the relevant discussion in the Introduction to enhance clarity and prevent\npotential misunderstandings.\n[Introduction]\nIn recent years, the rapid advancement of quantum mechanics1-3 has attracted increasing\nattention to the field of quantum information science4-6. As an interdisciplinary discipline\nbridging quantum physics and information science, quantum information science is\ntransforming research paradigms in both science and technology with its substantial practical\npotential and unique capabilities. Specifically, quantum communication7-10 leverages the\nphenomenon of quantum entanglement to ensure the security of information communication,\nwhereas quantum computation11-14 exploits the principle of quantum superposition to achieve\ncomputational power that surpass that of classical computers, thereby driving transformative\nadvances in fields of materials science, chemistry and beyond. Furthermore, the recent progress\nin quantum sensing15-18 and measurement19-21 technologies has significantly improved the\nperformance of traditional sensors and measurement systems to unprecedented levels.\nThe success of quantum information science has not only stimulated the flourishing of\nquantum optics22,23, but has also propelled the development of quantum metasurfaces24-27.\nMetasurfaces are planar artificial structures composed of subwavelength meta-atoms arranged\nin either periodic or aperiodic configurations28-32. However, most passive metasurfaces lack the\ncapability to reconfigure their electromagnetic (EM) functionality once fabricated33,34, which\nsignificantly limits their practical applications. To address this challenge, the concept of\nreconfigurable metasurfaces35-38 has been introduced. The switching capabilities of the\nelectromagnetic response in reconfigurable metasurfaces have motivated the development of\nthe digital metasurfaces39 and subsequently evolved into information metasurfaces40-48, which\nserve to bridge information science and classical electromagnetic physics.\nThe basic information-processing units of information metasurfaces are based on classical\ndigital bits, which offer benefits such as stability, ease of storage and transmission, and\nP\nA\nG\nE\noperational simplicity. However, they suffer from limitations in information capacity and\nparallel-processing capability. In contrast, quantum bits (qubits) 49-51 exhibit unprecedented\nsuperiority in these aspects, offering potential solutions to address the challenges currently\nfaced by classical digital bits. However, qubits are often unstable, difficult to store and transmit,\nand highly susceptible to environmental interference. To combine the respective advantages of\nclassical bits and qubits, several attempts are being made to develop quantum-inspired bits52,53\nin classical systems. Nevertheless, current studies are mostly limited to the theoretical\nexplorations, and the experimental realization and manipulation of quantum-inspired states in\nclassical systems remain a significant challenge in this field.\nP\nA\nG\nE"}, {"round": 2, "reviewer_comments": {"reviewer_3": "The Authors provided a detailed response to my comments, which is much appreciated. They performed a thorough\ncomparison with other works on tunable metasurfaces, which makes the benefits of their design clearer.\nHowever, in my honest opinion, they did not directly address my comment on the confusion they might create with the\nquantum terminology they rely on. The representation of elliptical polarization states as superposition of circular states is\nwell known in classical EM theory. Even the representation of polarization states on the Bloch sphere can be found in\nseveral optics textbooks. Although there are analogies with superposition states in quantum mechanics, such analogies are\nnot necessary to describe the effects presented in the paper. Following the same logic as the Authors, one could argue that\nany circularly or elliptically-polarized antenna with two feeding points and a phase shifter could be considered as generating\ntunable \"superposition or nonseparable states.\" Although, in some sense this could be considered true, such a description is\nalmost never used, because it creates more confusion that it clarifies the functionality of the antenna to generate classical\nelliptically-polarized waves.\nAs I mentioned in my original review, the main novelty of the paper is the presentation of metasurface designs that can\ndynamically convert a polarization state to any other polarization state. Aside the practical concerns related to the\nmechanical parts of the design, I think this achievement is by itself very interesting and unique. One could envision that\nsome day such metasurfaces could find applications in preparation of quantum states. However, this does not change the\nfact that this is not the case with the metasurfaces in the paper, which are designed to generate classical elliptical\npolarization states.\nEven if the Authors prefer using the \"superposition\" and \"nonseparable\" terminology, I think at least the title should clearly\nreflect the classical nature of the design. Also, I find the new discussion in the Introduction a bit vague and hand-wavy. For\nexample, the Authors write \"Hence, complex error correction techniques are required to compensate the limitation.\nConsequently, implementing their advantages in the classical systems becomes a feasible solution.\" What does it mean to\nimplement the advantages of qubits in the classical domain? Despite any similarities with quantum systems, no classical\nsystem can offer the benefits of quantum information systems, because classical systems do not violate Bell's inequalities."}, "author_response": "Authors’ Responses\nTO REVIEWER #3\nWe sincerely thank you for the time and effort invested in reviewing our manuscript and offering\nthe insightful comments and thoughtful suggestions. In particular, you stated that “The Authors\nprovided a detailed response to my comments, which is much appreciated. They performed a\nthorough comparison with other works on tunable metasurfaces, which makes the benefits of\ntheir design clearer. …. Aside the practical concerns related to the mechanical parts of the\ndesign, I think this achievement is by itself very interesting and unique. One could envision that\nsomeday such metasurfaces could find applications in preparation of quantum states.” These\ncomments and suggestions are extremely valuable to enhance the quality of our manuscript.\nFollowing your constructive feedback, we carefully revised the paper to improve its clarity and\ncomprehensibility. Below are our point-to-point responses to your comments.\nComment 1:\nAs I mentioned in my original review, the main novelty of the paper is the presentation of\nmetasurface designs that can dynamically convert a polarization state to any other polarization\nstate. Aside the practical concerns related to the mechanical parts of the design, I think this\nachievement is by itself very interesting and unique. One could envision that someday such\nmetasurfaces could find applications in preparation of quantum states. However, this does not\nchange the fact that this is not the case with the metasurfaces in the paper, which are designed\nto generate classical elliptical polarization states. Even if the Authors prefer using the\n\"superposition\" and \"nonseparable\" terminology, I think at least the title should clearly reflect\nthe classical nature of the design.\nResponse and Action Taken:\nThank you very much for your valuable suggestions. Following your recommendation, we\nhave revised the title of the manuscript to “Quantum-inspired superposition and nonseparable\nstates of reconfigurable metasurfaces in classical systems” to more clearly reflect the classical\nnature of the design.\n[Title]\nQuantum-inspired superposition and nonseparable states of reconfigurable metasurfaces in\nclassical systems\nFurthermore, we have carefully revised the main text and supplementary materials to\nreplace the “superposition state” and “nonseparable state” by “analog superposition state” and\n“analog nonseparable state,” respectively. We have also clarified that these states are\n“quantum-inspired” states that are implemented in the classical system rather than a\nP\nA\nG\nE\nquantum system. More details of our revision can be found below:\n[Abstract]\n Here, analog superposition states and analog nonseparable states are theoretically ...\n To implement these two quantum-inspired states in classical systems, we have developed\na reconfigurable time-varying metasurface capable of synthesizing analog superposition\nstates across the temporal dimension and analog nonseparable states across spatial and\npolarization dimensions. Due to its unique features of analog superposition and analog\nnonseparability, ...\n[Introduction]\n We should clarify that the quantum-inspired states discussed here are implemented in a\nclassical system rather than in a quantum system.\n the mathematical and geometric representations of the analog superposition state ...\n describe the analog superposition state, ...\n the concept and mathematical framework of the analog superposition state to explore the\nanalog superposition behavior of the EM waves based on the reconfigurable metasurface\nin a classical system ...\n which is a crucial ability to implement the analog superposition state. We further\ndemonstrate an analog nonseparable state that mirrors ...\n realize the concept of quantum-inspired states. ...\n[Reconfigurable time-varying metasurface]\n the state of which can be mathematically expressed as an analog superposition state: ...\n To implement the aforementioned analog superposition state, …\n Additionally, the metasurface exhibits analog nonseparable state properties, ...\n Given that the analog superposition state corresponds to the ...\n In our case, the analog superposition of states is implemented in ...\n In principle, minimizing the time interval towards zero would yield an analogue of the qubit\nsuperposition state. More details of the theoretical derivations for the mathematical and\ngeometric representations of the analog superposition state in ...\n[Reconfigurable time-varying meta-atom]\n the proposed theory of analog superposition states in reconfigurable time-varying\nmetasurfaces ...\n In order to ensure the reliability and accuracy of the analog superposition state in ...\n the geometric representation of the analog superposition state on ...\n From an application perspective, the analog superposition states in ...\n Further details on the broadband validation of the analog superposition state are ...\n both mathematical and geometric representations of analog superposition states in ...\n[Analog superposition state of reconfigurable metasurfaces in classical systems]\nP\nA\nG\nE\n here we study the analog superposition state in ...\n manipulate the analog superposition state of the ...\n To realize the analog superposition state in ...\n This allows to construct the analog superposition states on ...\n It should be noted that the analog superposition states have been ...\n on the performance of the analog superposition states is ...\n[Analog nonseparable state of reconfigurable metasurfaces in classical systems]\n To characterize the analog nonseparable states of space-polarization60,61 in ...\n to demonstrate the analog nonseparable correlation ...\n we can establish an analog nonseparable state based on ...\n exhibit an analog nonseparable state between ...\n Hence, we validate that an analog nonseparable state between ...\n[Experimental demonstration of reconfigurable time-varying metasurfaces]\n metasurface is capable of characterizing the analog superposition state to yield an analogue\nof the qubit superposition state, we ...\n the mathematical and geometric representations for the analog superposition state in ...\n be limited to the analog superposition states or analog nonseparable states at ...\n[Discussion]\n facilitating the exploration of analog superposition states and analog nonseparable states.\nIt should be noted that both investigations of the analog superposition states and analog\nnonseparable states at ...\n both mathematical and geometric representations of the analog superposition state within ...\n crafted for the analog superposition state. ...\n the geometric representation of the analog superposition state can be ...\n explore the potential for an analog nonseparable state of space-polarization between ...\n a feasible physical platform to implement the analog superposition state. ...\n[Methods]\n both analog superposition states and analog nonseparable states of ...\n The analog superposition properties of the meta-atoms were ...\n investigate the analog nonseparable state in ...\n It should note that the analog nonseparable state simulation ...\n[Fig.1]\n which exhibits an analog nonseparable state of space-polarization between ...\n[Fig.3]\n Analog superposition state in ...\n Since only the analog superposition state at the ...\n[Fig.4]\nP\nA\nG\nE\n Analog nonseparable state of space-polarization between ...\n[Fig.5]\n Experimental verification of the analog superposition state in ...\n of the analog superposition state in reconfigurable ...\n[Supplementary Section 1: Mathematical representation of the analog superposition state\nin reconfigurable time-varying metasurface]\n a mathematical portrayal of the analog superposition state in ...\n the mathematical representations of the analog superposition state derived ...\n[Supplementary Section 2: Theoretical framework for the analog nonseparable state in\nreconfigurable time-varying metasurface]\n To characterize the analog nonseparable state in ...\n takes an analog nonseparable form representing ...\n[Supplementary Section 5: Experimental setup for verifying the analog superposition\ncharacteristics in reconfigurable time-varying metasurface]\n validations of all analog superposition properties within ...\n verifying analog superposition characteristic in ...\n[Supplementary Section 7: Impact of different polarizations and angles of incident wave\non analog superposition state in reconfigurable time-varying metasurface]\n and their analog superposition state, we ...\n the mathematical representation of the analog superposition state is ...\n[Supplementary Section 9: Fidelity of the analog superposition state in reconfigurable\ntime-varying metasurface]\n mathematical representation of the analog superposition state in reconfigurable ...\n[Supplementary Section 11: The influence of lattice geometries on the properties of meta-\natoms]\n can also achieve the analog superposition state, as ...\n higher precision in controlling the analog superposition state in ...\n[Supplementary Section 12: Broadband validation of the analog superposition state in\nreconfigurable time-varying metasurface]\n geometric representation of the analog superposition state in ...\n characterizing the analog superposition state’s geometric representation ...\nComment 2:\nAs I mentioned in my original review, the main novelty of the paper is the presentation of\nmetasurface designs that can dynamically convert a polarization state to any other polarization\nstate. Aside the practical concerns related to the mechanical parts of the design, I think this\nachievement is by itself very interesting and unique. One could envision that someday such\nmetasurfaces could find applications in preparation of quantum states. However, this does not\nchange the fact that this is not the case with the metasurfaces in the paper, which are designed\nto generate classical elliptical polarization states. Even if the Authors prefer using the\n\"superposition\" and \"nonseparable\" terminology, I think at least the title should clearly reflect\nthe classical nature of the design.\nResponse and Action Taken:\nWe appreciate your valuable feedback and sincerely apologize for any ambiguity arising\nfrom our initial discussion in the Introduction. In response to your suggestions, we have\nthoroughly revised the relevant discussion in the Introduction to enhance clarity and prevent\npotential misunderstandings.\n[Introduction]\nIn recent years, the rapid advancement of quantum mechanics1-3 has attracted increasing\nattention to the field of quantum information science4-6. As an interdisciplinary discipline\nbridging quantum physics and information science, quantum information science is\ntransforming research paradigms in both science and technology with its substantial practical\npotential and unique capabilities. Specifically, quantum communication7-10 leverages the\nphenomenon of quantum entanglement to ensure the security of information communication,\nwhereas quantum computation11-14 exploits the principle of quantum superposition to achieve\ncomputational power that surpass that of classical computers, thereby driving transformative\nadvances in fields of materials science, chemistry and beyond. Furthermore, the recent progress\nin quantum sensing15-18 and measurement19-21 technologies has significantly improved the\nperformance of traditional sensors and measurement systems to unprecedented levels.\nThe success of quantum information science has not only stimulated the flourishing of\nquantum optics22,23, but has also propelled the development of quantum metasurfaces24-27.\nMetasurfaces are planar artificial structures composed of subwavelength meta-atoms arranged\nin either periodic or aperiodic configurations28-32. However, most passive metasurfaces lack the\ncapability to reconfigure their electromagnetic (EM) functionality once fabricated33,34, which\nsignificantly limits their practical applications. To address this challenge, the concept of\nreconfigurable metasurfaces35-38 has been introduced. The switching capabilities of the\nelectromagnetic response in reconfigurable metasurfaces have motivated the development of\nthe digital metasurfaces39 and subsequently evolved into information metasurfaces40-48, which\nserve to bridge information science and classical electromagnetic physics.\nThe basic information-processing units of information metasurfaces are based on classical\ndigital bits, which offer benefits such as stability, ease of storage and transmission, and\nP\nA\nG\nE\noperational simplicity. However, they suffer from limitations in information capacity and\nparallel-processing capability. In contrast, quantum bits (qubits) 49-51 exhibit unprecedented\nsuperiority in these aspects, offering potential solutions to address the challenges currently\nfaced by classical digital bits. However, qubits are often unstable, difficult to store and transmit,\nand highly susceptible to environmental interference. To combine the respective advantages of\nclassical bits and qubits, several attempts are being made to develop quantum-inspired bits52,53\nin classical systems. Nevertheless, current studies are mostly limited to the theoretical\nexplorations, and the experimental realization and manipulation of quantum-inspired states in\nclassical systems remain a significant challenge in this field.\nP\nA\nG\nE"}, {"round": 3, "reviewer_comments": {"reviewer_3": "The Authors revised the paper to make the classical nature of their structure clear. The motivation and terminology are in my\nopinion still unnecessarily complicated, but I recognize that this can also be a matter of personal preference and I will not\ninsist further on this."}, "author_response": ""}]

Decision letter