Entanglement-inspired frequency-agile rangefinding

Domain: physics
Published: 2026-01-24
Editorial outcome: minor_revision

Abstract
Entanglement, a key feature of quantum mechanics, is recognized for its non-classical correlations which have been shown to provide significant noise resistance in single-photon range finding and communications. Drawing inspiration from the advantage given by energy-time entanglement, we developed an energy-time correlated source based on a classical laser that preserves the substantial noise reduction typical of quantum illumination while surpassing the quantum brightness limitation by over six orders of magnitude, making it highly suitable for practical remote sensing applications. A frequency-agile pseudo-random source is realized through fiber chromatic dispersion and pulse carving using an electro-optic intensity modulator. Operating at a faint transmission power of 48 μW, the distance between two buildings 154.8182 m apart can be measured with a precision better than 0.1 mm, under varying solar background levels and weather conditions with an integration time of only 100 ms. These trials verified the predicted noise reduction of this system, demonstrating advantages over quantum illumination-based range finding and highlighting its potential for practical remote sensing applications.

Introduction
Quantum entanglement has been widely explored for its potential to improve performance in the fields of communication1,2, computing3,4, sensing5–9 and imaging10,11. In the field of quantum metrology, the method offers advantages including enhanced precision12–14 and noise suppression15–19, which are particularly critical in remote sensing under challenging conditions, such as strong background and increased transmission loss. Since Lloyd’s pioneering work in 200820, quantum illumination has garnered significant attention for its superior noise reduction capabilities in noisy and lossy environments. This improvement is primarily attributed to the entanglement and correlation properties of photon pairs21,22. Lloyd’s theory projected that using n-dimensional entangled photon states could reduce noise compared to unentangled single-photon states. Subsequent studies18,23,24 have explored splitting quantum sources into n frequency modes, allowing quantum systems to filter out unentangled noise via energy-time entanglement measured using joint detection, and demonstrating an enhanced signal-to-noise ratio (SNR).

However, applying quantum illumination to practical target detection presents significant challenges25,26. Generating, maintaining and detecting entangled photon pairs are more complex processes than their classical analogues, making quantum setups less robust. For instance, entanglement-based detection can require quantum memory to store the reference photon, complicating the detection platform and requiring prior knowledge of the target’s distance, which limits its applicability in range finding. The target in any range finding demonstration is a classical object that is either there or not, which in the language of quantum information means it is in the computational basis. As such, correlation measurements (without entanglement) can retain the key noise-reduction benefits while simplifying the system24,27,28. These advancements eliminate the need for pre-existing range information and quantum memory, making the setup more practical for distance measurement. Typical setups generate correlated photon pairs using a nonlinear crystal18,24,29,30 or semiconductor optical chip15, sending one photon of each pair (signal) to the target while keeping the other (idler) as a reference. Range can then be measured using time differences between the two photons of each pair. Uncorrelated noise is filtered out via energy-time correlations, noticeably boosting detection sensitivity.

Despite these improvements, the brightness of photon-pair sources remains a significant limitation. Brightness is critical for remote target detection, as the number of detected back-scattered photons diminishes quadratically with distance, and at longer ranges, this can extend to a quartic relationship due to light divergence. The brightness of commonly used spontaneous parametric down-conversion (SPDC) sources is inherently limited by multi-photon emission, which when avoided results in low emission rates. Semiconductor quantum dot sources offer more efficient photon generation, but extracting photons is still challenging due to the high refractive index of surrounding materials31. Additionally, the maximum detection rate is constrained by the number of photons per time resolution window (typically > 100 ps). For example, with correlated photon pair emission into n modes and detection using n single-photon detectors, the maximum count rate can reach 1010 photons per second (assuming n = 10 and 0.1 pairs per detection window). This limits the maximum system loss to ~ 80 dB, considering an overall system efficiency of − 20 dB, which restricts the practical use of quantum illumination in remote sensing. In contrast, classical sources can easily achieve many orders of magnitude higher brightness levels32,33, making them more suitable for long-range detection. For example a 600 mW average power laser with a repetition rate of 500 kHz results in 1013 photons per pulse, has been reported for imaging over 200 km33.

Recent research has explored the idea of using energy-time correlations from coherent sources to maintain quantum-like advantages34–36. However, these systems rely on nonlinear properties, which introduce a similar complexity to quantum sources and confine the detection range to be within the coherence length. As a result, all of them are demonstrated under controlled laboratory conditions and are difficult to extend to real-world remote sensing.

To address these limitations, we have developed a robust system that generates energy-time correlations without requiring a frequency conversion process, by modulating a classical source. This quantum-inspired range finding employs classically correlated optical sources while preserving most of the noise-reduction benefits of quantum range finding, which uses entangled-photon sources. To achieve the benefit of entanglement requires operating at the time-bandwidth limit at low photon numbers per timing window, limiting operational distance22. This approach validates our theoretical model (Eq. S10 in Supplementary Section II) where we find that the SNR simplifies to

SNR = S / \sqrt{S + D + B} = n / \sqrt{n + B/n} (1)

where S, D and B are the total correlated signal counts, dark counts and background counts across all channels. We clearly see that the dark and background counts are suppressed by using multiple channels n, resulting in an enhanced SNR (see Supplementary Section II for full derivation). Using a three-channel (n = 3) frequency-agile correlated source based on fiber chromatic dispersion, we demonstrate noise reduction through field trials under various weather conditions over distances of more than 150 m. With the transmitter power attenuated to less than 50 μW the system shows potential for eliminating crosstalk in multi-use conditions, or for covert illumination, while demonstrating significantly higher brightness than entangled photon sources. Notably, the source power can be easily increased, making it suitable for longer-range measurements and showing that the brightness limitations of quantum systems can be bypassed without sacrificing noise suppression.

Results
Energy-time correlations in our quantum-inspired source are built up by stretching femtosecond laser pulses to nanosecond scale using fiber chromatic dispersion then pulse carving to create three frequency channels as described in the Methods section and illustrated in Fig. 1. Figure 2a and b display the characterization of the created correlation with respect to time and energy, respectively. The gray area with a black line represents the stretched pulse of the primary fs-laser before temporal modulation, while the colored areas correspond to the three selected channels after electro-optic intensity modulator (EOIM) modulation. Figure 2a demonstrates the time-domain selection and separation of the three channels by applying different time delay windows to the stretched pulse. Figure 2b shows the energy separation of the three channels, characterized by their spectra with central wavelengths of 1532.2 nm, 1562.5 nm, and 1583.7 nm. The direct correspondence between the pulse time sequence and the increasing wavelength spectra demonstrate the successful creation of energy-time correlation across the three channels. The three wavelengths are selected using a pseudorandom sequence of length 10 μs to allow unaliased range finding up to 1.5 km distance. After successfully creating three separate wavelengths by time-gating, the short pulse is reformed in a grating-based compressor.

The quantum-inspired correlation source can achieve an average power of 147.5 μW before the fiber splitter, corresponding to 1.15 × 1015 photons per second. This represents more than 60 dB improvement compared to conventional quantum sources of 1 × 109 photons per second assuming 0.1 photon pairs per time window (100 ps) on average24. This significant enhancement in source brightness has enabled us to extend the detection distance from several meters in the lab24 to field trials conducted between two buildings, separated by a distance of over 150 m.

The results from night-time measurements, where photons were scattered back from the external wall of Wills Memorial building (WMB) with an integration time of one second, are shown in Fig. 3. Figure 3a presents the photon-counting histograms of return photons in three channels within one source period of 20 ns. The leftmost peaks of the three channels are the main return signals and are well aligned with each other, indicating that the energy-time correlation has been effectively concealed by the grating-based compressor. The right peaks are the breakthrough from the EOIM caused by reducing the repetition rate from 100 to 50 MHz. This leakage arises from the relatively low EOIM extinction ratio, which is due to the broadband spectra in each channel. This issue could be mitigated by increasing the number of channels, thereby narrowing the spectral width of each channel. Figure 3b shows a 200 ns excerpt of a 10 μs long photon-counting histogram, triggered by the start of the random pattern. Transmission losses scattered from the Lambertian target were calculated to be 98.1 dB in this experiment, resulting in a maximum count rate of only 6 photons per time bin, some of which may include background noise or detector dark counts. The smaller peaks with counts around one photon are due to leakage from the EOIM, dark counts, and background noise. By post-selecting the encoded timing information, we can identify that peak 1 corresponds to the echo signal, peak 2 is EOIM leakage, and peak 3 is detector dark counts. Given the night-time conditions, the background noise level was low and can be considered negligible.

Distance information was extracted from the photon-counting histograms of the return signal using the coincidence-based correlation method. The coincidence counts in each channel were calculated by cross-correlating the normalized reference, made up of the random channel sequence repeating for the chosen integration time, with the echo photon counts for each channel, resulting in three-channel coincidence counts shown in Fig. 3c. From this data the round-trip time was estimated from the location of the highest peak, and the corresponding range was calculated using the formula r = ct/2, where c is the speed of light and t is the round-trip time of the illuminating photons. Magnifying the peak region in the inset, several periodic side peaks can be observed. The relatively high side peaks are due to the 50 MHz pulse repetition period, while the smaller peaks arise from leakage of the 100 MHz pulse. The measured peak (with a time bin of 50 ps) was fitted using a Gaussian function (see Fig. 3d), centered at a distance of 154.81822(5) m. This fitting improves the measurement precision to ± 48 μm, representing the statistical uncertainty in locating the peak centroid and overcoming the limitations set by detector jitter. In contrast the single shot depth resolution is determined by the full width at half maximum (FWHM) of combined the three-channel histogram shown in Fig. 3d, which is 25.7(1) mm. This value indicates how well two targets at different depths can be distinguished. Additionally, the unambiguous range was extended from 3 m to 1500 m, set by the length of the random channel sequence. This breaks the limit of a periodic source on maximum unambiguous detection distance37, caused by the high repetition rate of 50 MHz, and could be further extended using a longer random sequence or even a real-random sequence.

To experimentally validate the theoretical model that shows a significant noise reduction effect from using multiple energy channels, we compared a one-channel (n = 1), two-channel (n = 2) and three-channel (n = 3) system under varied solar background levels using data from three single-photon detectors. Since the periodic peaks are primarily due to the source repetition rate, we focused on the range peak region within a 1.5 m (10 ns) window, excluding the influence of the periodic signal.

First, coincidence-based correlated counts Cij were calculated between the normalized reference channel i and detected photon channel j (i, j ∈ A, B, C) using data collected during the daytime with 1 s integration time, as displayed in Fig. 4a. Here, correlated elements occur when i = j, and uncorrelated elements occur when i ≠ j. For single-channel measurements (n = 1), no energy-time correlation exists, meaning all elements are considered:

C total,n=1 = (C AA + C AB + C AC + C BA + C BB + C BC + C CA + C CB + C CC) (2)

For two-energy channels (n = 2), two of the three photon detection channels (e.g., A and C) are treated as one combined channel. The correlated counts between this combined channel and the third channel (e.g., B) are calculated as follows:

C total,n=2 = (C AA + C AC + C CA + C CC) + C BB (3)

Finally, for three-energy channels (n = 3), the correlated counts for all three channels are given by:

C total,n=3 = C AA + C BB + C CC (4)

As illustrated in the correlation tomography of Fig. 4c and d, the signal and noise counts were extracted from Fig. 4a by integrating the peak region, with the average noise level subtracted (orange area) and the fluctuating region, estimated as the average noise level multiplied by the integration time (blue area). In Fig. 4c, the signal counts primarily come from correlated elements (i = j), indicating low crosstalk across multiple energy channels. Uncorrelated counts (i ≠ j) are filtered or different selection methods such as those discussed below and in Supplementary Section VII. Notably, the signal displayed in the correlation tomography (Fig. 4c) has been background-subtracted to reflect the net signal used in the SNR calculation Eq. (1). As shown in Eqs. (2), (3), and (4), the signal remains nearly constant across different configurations due to low crosstalk. In contrast, the background counts depicted in Fig. 4d are comparable between the correlated and uncorrelated elements, indicating that the total noise decreases approximately proportionally to the number of channels (n), owing to the reduced number of contributing elements in the noise term.

Based on the above processing, the SNR of range finding systems with varying channel numbers (n ∈ 1, 2, 3) was measured with one-second integration under different levels of solar background during daylight, as demonstrated in Fig. 4b. The experimental data, marked as symbols with different colors, were fitted to our theoretical model (Supplementary Section II), with colored curves representing different channel numbers (n). The agreement between the model and field trial results demonstrates the validity of the theoretical framework. The SNR improves with an increasing number of channels, particularly under higher background rates. A more pronounced noise reduction can be realized by extending the channel quantity to 80, as indicated by the purple theoretical dashed curve, with an enhancement of 5.7 dB at the maximum detected solar background level of 565 kcounts/s. Practical realization can be achieved through large-scale photonic integration combined with off-chip commercial dense wavelength division multiplexing (DWDM) components and detector array technology (Supplementary Section VII).

Experimental results under various weather conditions conducted on the same day are presented in Fig. 5. Figure 5a–d display photos of the WMB taken from Queens Building Balcony (QBB), along with the corresponding weather conditions and detected total background counts from three single-mode fiber coupled single-photon detectors. Figure 5e–h show the return photon histograms for each channel, integrated over 100 ms and displayed within a period of 20 ns. During nighttime, the echo photon peak is notably clear, with an extremely low noise level in Fig. 5e, corresponding to a distinct range peak centered at 154.81822(5) m (Fig. 5i). Although the building appears colorful at night in Fig. 5a due to visible light illumination, its influence on noise counts is negligible, as the visible light is filtered out by a long-pass filter and cannot be detected by the InGaAs single-photon detectors. During rainy moments, the detected background level increased to 8.5 kcounts/s, resulting in a dark appearance of the building in Fig. 5b. Consequently, the noise level in the photon counting histogram (Fig. 5f) rises, while the signal peak slightly decreases due to higher transmission loss from the raindrops. As shown in Fig. 5j, the influence on the range peak becomes apparent, evidenced by the reduction of peak intensity. Under cloudy conditions, with measured background counts reaching 370 kcounts/s, the building appears brighter compared to the rainy period, as depicted in Fig. 5c. The background intensity in both photon-counting histogram (Fig. 5g) and correlated photon histogram (Fig. 5k) increases. However, the signal peak (after subtracting the noise level) is diminished due to the elevated background level. When sunlight illuminates the building at sunrise, as shown in Fig. 5d, the three signal peaks in the photon-counting histogram (Fig. 5h) become indistinguishable due to strong solar background noise. Nevertheless, the range peak remains detectable with the three-channel platform, while the single-channel peak becomes challenging to resolve (Fig. 5l). By comparing results from different numbers of energy channels, significant noise suppression is observed with the three-channel peak (n = 3), particularly under sunny conditions with higher background counts (Fig. 5l). The corresponding simulation results using the measured solar background level are shown in Fig. 5m–p. The SNR is increased significantly with longer distance measurements due to increased transmission loss, especially under strong background levels. It should be noted that the current system can be further optimized through reductions in transmission losses and increased source power, potentially extending the detection range beyond 1 km.

Methods
Entanglement-inspired source
A schematic of our system is depicted in Fig. 1a. We used a fiber laser to create 58 fs long pulses at a repetition rate of 100 MHz with a central wavelength of 1563 nm and a spectral width of 67 nm. The power was carefully controlled using a fiber-coupled digital variable attenuator. The short pulses were temporally stretched to 1.2 ns using a 1 km long telecommunication band single-mode fiber (SMF28). After passing through a fiber polarization controller, the pulse was directed to an EOIM for energy channel selection. Based on the fiber chromatic dispersion, three wavelength channels were picked up within 250 ps time windows distributed over the 1.2 ns pulse duration, allowing for precise channel selection via different time delays processed by a field-programmable gate array (FPGA). The electrical signal processing is detailed in Supplementary Section III. By encoding a pseudo-random pattern to the time delay in the electrical signal, wavelength channels were randomly selected. Using this method, energy-time correlations were successfully generated from a classical source. The pulse was then split by a 1 × 2 fiber coupler with a coupling ratio of 50:50, with one path directed to a grating-based compressor used to erase the channel-selection information for covert sensing and improving distance measurement resolution. The other path was either detected by a fiber-coupled InGaAs photodiode (Thorlabs DET08CFC) connected to a fast oscilloscope (KEYSIGHT DSO-S 404A) for real-time performance monitoring, or sent directly to an optical spectrum analyser (OSA) for spectral analysis.

Field trial of entanglement-inspired range finding
By integrating the developed source into a range finding platform, the signal was transmitted through a single-mode fiber to a collimator positioned on the QBB, as depicted in Fig. 1b. The average transmitter power was attenuated to 48 μW for the field trial. The system had a full beam divergence of 0.032° (0.56 mrad), and the signal illuminated the external wall of WMB, approximately 154.8 m away from QBB, as shown in Fig. 1c. The measured distance, shown in Fig. 1d, was determined using a commercial range finder with a resolution of 0.1 m. The backscattered light from the building was collected by a 48 mm telescope and coupled into a single-mode fiber, passing through a long-pass filter at 1500 nm to block visible and near-infrared solar background. This filtered signal was split by a wavelength division multiplexer (WDM) and directed into three infrared single-photon detectors (ID230) through single-mode fibers, as illustrated in Fig. 1a. These InGaAs/InP photon detectors, set with a 2 μs dead time and 15% quantum efficiency, sent their detected signals to a Time Tagger (Picoquant HydraHarp 400), synchronized with the beginning of the repeating pattern down-converted by the FPGA. The field trial ran continuously from night through to day under varying weather conditions, enabling us to perform a comparison of the experimental results with our noise-reduction theory.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors have reported a LIDAR system enabled by time-energy correlations engineered in a modulated classical pulse.\nUnlike time-energy correlations in biphotons generated through nonlinear processes, the current approach is not limited by\nthe poor efficiency of nonlinear processes or the need to operate in the low-gain regime to maintain these correlations. The\nauthors show that using an n-channel coincidence detection scheme, the noise rejection increases with increasing number\nof channels n, leading to an improved signal-to-noise ratio. The authors demonstrate range measurements between two\nbuildings, separated by 154 and 413 m, with an accuracy of 0.1 mm and a measurement time of 0.1 s.\nThe work is very well written and well presented. The conclusions are sound, and the arguments are very well laid out. I\nhave a few questions and comments for the authors.\n- What is the relation between the randomness of the modulation sequence and the detection distance? I didn't understand\nthe link in line 226.\n- In Figure 4, the shading in the signal box makes it impossible to see that there are 3 peaks. I recommend using an unfilled\nbox to highlight this region. Similarly, the noise box colour blue is the same as the trace for C_AC and should be changed.\n- I did not understand the improvement factor of 10^6 compared to quantum sources. The authors should clarify how they\narrive at this number.\n- The numbers in lines 453-468 seem a little random. While I appreciate that these are the experimental parameters, it would\nhelp the reader to understand whether these are chosen for a specific purpose or imposed by equipment limitations. This\ncan be done in a Supplementary document.\n- How would this technique compare to a direct range-finding approach using the output from the laser (pulse duration,\nrepetition rate at the same average power) and a single detector? This would allow for a much narrower coincidence\nwindow, reducing the background and the dark counts. Would that be equivalent to the n=1 case?\nOverall, I would recommend the manuscript for publication as it demonstrates clear novelty and enhanced capabilities in\nquantum-inspired sensing.\nBienvenu Ndagano", "reviewer_2": "This paper introduces a method for long-range, low-power optical rangefinding that leverages classical laser systems to\nemulate the noise-resilience typically associated with quantum illumination. The approach exploits energy-time correlations\ngenerated via fiber-induced chromatic dispersion and electro-optic intensity modulation. The authors demonstrate sub-\nmillimeter ranging precision at distances exceeding 150 meters, all while operating under low transmission power, with\npromising potential for scalability in both range and performance.\nHowever, in my view, the manuscript does not meet the significance threshold required for publication in Nature\nCommunications. The novelty and impact of the work are limited when considered in the context of the current state of the\nfield and the existing literature. A more technically focused journal may provide a more appropriate venue for this work.\n-------------------------------------\nGeneral Comments:\n1. A central conceptual pillar of this work is its framing as \"quantum-inspired.\" The authors assert that the system inherits the\nnoise-reduction benefits of quantum illumination — particularly those coming from energy-time entangled photon pairs —\nwithout relying on actual entanglement. This distinction, however, is blurred throughout the manuscript.\n2. While it is true that structured correlations in time and frequency can mimic certain behaviors seen in quantum systems,\nthe correlation mechanism here is entirely deterministic and rooted in classical signal engineering. The authors do not\nsufficiently delineate the theoretical boundary between what is \"quantum-like\" in behavior and what is simply classical\nmodulation and post-processing. Without any true non-classical light source or statistics being involved, referring to the\nmethod as \"quantum-inspired\" risks overstatement.\n3. One important question that arises is whether the classical correlations employed here replicate the information-theoretic\nand physical properties (such as resilience to loss, indistinguishability under thermal noise, and robustness against entropic\ndecoherence) that define true quantum illumination. The paper does not explore the theoretical limits of its system in\ncomparison to, for instance, the optimal bounds predicted by quantum Fisher information theory or Holevo capacities. As\nsuch, while the system borrows intuitions from quantum mechanics, it is not clear to what extent those benefits are\nfundamental versus incidental.\n4. The authors derive and experimentally validate a SNR model in which dark and background noise contributions are\nsuppressed by increasing the number of independent energy-time channels. While the data presented does support a trend\nof noise suppression, the analytical model assumes ideal separation between channels and uncorrelated noise across\nthem. In real systems, however, factors such as timing jitter, spectral bleed, channel crosstalk, and detector afterpulsing can\nerode the orthogonality and independence assumptions underpinning this model.\n5. I am a bit confused about the measurement. The experimental implementation uses three channels, the authors\nextrapolate their model to predict substantial benefits at 80 channels using commercial DWDM components. No information\nis provided about how increasing channel count affects the complexity, calibration difficulty, or cross-channel\nsynchronization of the system. Practical deployment of an 80-channel version would face significant scaling challenges in\nterms of detector number, optical filtering precision, and FPGA control logic.\nThus, while the observed noise suppression is genuine within the limited configuration tested, the scalability argument\nneeds more substantiation — particularly given that real-world LIDAR applications demand robust and cost-efficient\ndesigns.\n6. The authors report high range precision — down to ±48 µm — by performing Gaussian fits to the correlation peak in\naggregated histograms. While this is technically accurate, it is important to distinguish between measurement precision (how\nconsistently one can locate the peak centroid) and resolution (how well two targets at different depths can be resolved). The\nFWHM of the system’s impulse response, which defines depth resolution in practical terms, remains on the order of 25 mm.\n7. One of the major weaknesses of the manuscript is the lack of systematic benchmarking against state-of-the-art classical\ntechnologies. The only substantive comparisons are made with quantum rangefinding systems based on SPDC, which are\ninherently limited by low brightness and high experimental fragility, especially in daylight.\nThe high-performance LIDAR systems based on time-correlated single-photon counting, frequency-modulated continuous\nwave principles, and pulsed illumination with GHz detection bandwidths have made significant progress in long-range\ndetection, noise rejection, and covert operation. Many of these use sophisticated coding schemes and multi-channel\napproaches not dissimilar in spirit to what is proposed here.\n8. The paper makes a compelling case that the use of ultra-low transmission power and pseudo-random coding enables\ncovert rangefinding. While the low-power operation is evident, the claim of covertness is only speculative. No data or\nanalysis is provided to show how detectable (or undetectable) this system would be in practice against standard detection\ntools like optical time-domain reflectometers or RF/optical side-channel analyzers.\n9. The experimental demonstration is undoubtedly impressive, particularly the ability to measure distances with sub-mm\naccuracy across a 150–400 meter baseline in varying weather and lighting conditions. However, the paper will benefit from\nadditional discussion of environmental robustness — for example, whether alignment drift, thermal effects, or fiber movement\ndegrade performance. Additionally, long-term stability tests and repeatability of precision across independent trials are not\ndiscussed."}, "author_response": "Response to Reviewers’ Comments:\nReviewer #1 (Remarks to the Author):\nThe authors have reported a LIDAR system enabled by time-energy correlations engineered in\na modulated classical pulse. Unlike time-energy correlations in biphotons generated through\nnonlinear processes, the current approach is not limited by the poor efficiency of nonlinear\nprocesses or the need to operate in the low-gain regime to maintain these correlations. The\nauthors show that using an n-channel coincidence detection scheme, the noise rejection\nincreases with increasing number of channels n, leading to an improved signal-to-noise ratio.\nThe authors demonstrate range measurements between two buildings, separated by 154 and\n413 m, with an accuracy of 0.1 mm and a measurement time of 0.1 s.\nThe work is very well written and well presented. The conclusions are sound, and the\narguments are very well laid out. I have a few questions and comments for the authors.\nWe sincerely thank the reviewer for the positive comments on our manuscript, as well as for\nthe thoughtful questions and constructive suggestions, which help us to further clarify and\nstrengthen the work. Our detailed responses to each point are provided below.\n1.1 What is the relation between the randomness of the modulation sequence and the\ndetection distance? I didn't understand the link in line 226.\nResponse:\nThe detection distance is inherently limited by the repetition rate when a periodic pulsed laser\nis used as the source in a time-of-flight measurement. The distances can only be determined\nunambiguously when the pulse repetition rate is sufficiently low to ensure that only one pulse\nis in transit at any given time, limiting the source brightness. In other words, if the return signal\nfrom a distant target arrives after the next pulse has been emitted, the system cannot\ndetermine which emitted pulse it corresponds to, leading to range ambiguity. The maximum\ndistance at which pulses can be uniquely identified, known as the unambiguous range, is given\nby [1]\nc\nR = \nunambiguous 2∙f\nwhere f is the laser repetition rate and c is the speed of light. In our system, the original laser\noperates at a repetition rate of 50 MHz (after processing by the FPGA limited by the time-\ndelay module), corresponding to an unambiguous range of only 3 m.\nTo overcome this limitation, we employ a pseudo-random channel sequence (PRCS) of length\n500 by applying fibre-induced chromatic dispersion and pulse carving for wavelength-channel\nencoding in the developed source. This encoding effectively increases the unambiguous range\nto 1500 m, as the return signals can be uniquely identified based on their wavelength-\ndependent timing positions. Consequently, this approach extends the unambiguous detection\ndistance while maintaining accurate signal recognition. For clarity, we have revised the\ncorresponding sentences in the manuscript and included an additional reference, as shown\nbelow.\nThe revised version:\nLines 236 - 240: This breaks the limit of a periodic source on maximum unambiguous detection\ndistance [1], caused by the high repetition rate of 50 MHz, and could be further extended using\na longer random sequence or even a real-random sequence.\n[1] Krichel, N. J., McCarthy, A. & Buller, G. S. Resolving range ambiguity in a photon counting\ndepth imager operating at kilometer distances. Opt. Express 18, 9192-9206 (2010).\n1.2 In Figure 4, the shading in the signal box makes it impossible to see that there are 3\npeaks. I recommend using an unfilled box to highlight this region. Similarly, the noise box\ncolour blue is the same as the trace for C_AC and should be changed.\nResponse:\nWe thank the reviewer for this helpful suggestion. We have removed the shading in both the\nsignal and noise boxes to improve visibility in Fig. 4(a). To avoid colour overlap, the noise box\ndashed outline has been changed to a dark blue colour (Fig.4(a)). In addition, we have replaced\nthe word “noise” with “background” in Figs. 4(a) and (c) to avoid confusion between noise and\nsolar background, where noise refers to fluctuations and background denotes solar photon\ncounts collected by the single-photon detectors.\nThe revised version: The revised figure is shown below for clarity.\n1.3 I did not understand the improvement factor of 10^6 compared to quantum sources.\nThe authors should clarify how they arrive at this number.\nResponse:\nWe appreciate the reviewer’s careful evaluation and the emphasis on the improvement factor,\nwhich refers to the brightness enhancement of the developed source. The quantitative\nimprovement is described in the Results section, where we state:\n“The quantum-inspired correlation source achieves an average power of 147.5 μW before the\nfibre splitter, corresponding to 23 million photons per pulse. This represents more than 60 dB\nimprovement compared to conventional quantum sources that are forced to operate at one\nphoton per time window on average.”\nThe brightness of the quantum-inspired source is calculated from its achievable average\npower of 147.5 μW, corresponding to approximately 1.15 x 1015 photons per second. In\ncomparison, a conventional quantum source operating 0.1 pairs per time window (normally >\n100 ps) has a max brightness of 1 x 109 photons per second. This demonstrates an\nenhancement of more than 60 dB in brightness. To improve clarity, we have revised the\ncontent in lines 163-170 and also replaced the improvement factor to 60 dB in Discussion (line\n378-382).\nThe revised version:\n1. Lines 163-170: The quantum-inspired correlation source can achieve an average power\nof 147.5 μW before the fibre splitter, corresponding to 1.15 x 1015 photons per second.\nThis represents more than 60 dB improvement compared to conventional quantum\nsources of 1 x 109 photons per second assuming 0.1 photon pairs per time window (100\nps) on average.\n2. Lines 378-382: The developed source achieves a brightness enhancement of more\nthan 60 dB relative to conventional quantum sources, …\n1.4 The numbers in lines 453-468 seem a little random. While I appreciate that these are\nexperimental parameters, it would help the reader to understand whether these are chosen\nfor a specific purpose or imposed by equipment limitations. This can be done in a\nSupplementary document.\nResponse:\nWe appreciate the reviewer’s suggestion. The relevant content has been revised to better\nexplain the selection purpose and relocated to the Supplementary Section III.\nThe revised version:\n1. Add a sentence in the manuscript (lines 486-487): The electrical signal processing is\ndetailed in Supplementary Section III.\n2. Original lines 501-517 in main manuscript are relocated to Supplementary\ninformation Section III:\nElectrical Signal Processing: To realize precise energy channel selection, the EOIM is\ndriven by a 250-ps electrical signal with a variable time delay programmed by the FPGA\n(Xilinx ZYNQ-7000). The original electrical pulse is derived from the femtosecond laser\nto ensure synchronization, featuring a pulse width of 370 ps and a repetition rate of\nreliably detected by the FPGA input, and are then down-converted to 50 MHz, as\nconstrained by the operating range of the FPGA’s IDELAY module. A pseudo-random\nsequence of variable time delays is generated and encoded by the internal IDELAY\nmodule onto 500 consecutive pulses, synchronized with the down-converted 100-kHz\nreference signal sent to the time-tagger (HydraHarp 400). Finally, the electrical pulses\nare compressed to 250 ps (to enhance temporal resolution) and amplified to 3 V (to\nimprove the extinction ratio, though still below the full 6 V drive limit due to amplifier\nsaturation). These pulses are then applied to the EOIM, which serves as a high-speed\noptical switch that randomly selects wavelength channels according to the encoded\npattern.\n1.5 How would this technique compare to a direct range-finding approach using the\noutput from the laser (pulse duration, repetition rate at the same average power) and a single\ndetector? This would allow for a much narrower coincidence window, reducing the\nbackground and the dark counts. Would that be equivalent to the n=1 case?\nResponse:\nWe thank the reviewer for this insightful question, which highlights the key aspect of our work.\nTo demonstrate the noise-reduction advantage, we experimentally compared our method\nwith a direct rangefinding approach corresponding to the n = 1 case with the same detector,\nsame average source power and repetition rate, same pulse duration, as well as the same\non/off ratio of the pseudo-random pattern used to avoid the 3-metre unambiguous-range\nlimitation of the 50-MHz output laser.\nRegarding the coincidence window, it remains identical to that used in the multi-channel\nsystem since the laser pulse duration and detector timing jitter are the same. Therefore, the\nbackground and dark counts cannot be reduced by coincidence gating alone. In contrast, the\nbackground level increases because the collected photon counts are not filtered through\nenergy-time correlations. In other words, uncorrelated photon counts are fully detected,\nleading to a significant rise in background noise as illustrated in Fig. 4, where all uncorrelated\nphoton counts are included in the direct rangefinding case.\nWe appreciate the reviewer’s comment and have added a clarifying sentence in the revised\nmanuscript to better connect the concept of direct rangefinding with the n = 1 case.\nThus, we have proved our technique works with the present pulse width and detector jitter\nwithout broadening the coincidence window significantly. If we were to implement it with\nbetter detectors and shorter pulses, an n = 3 system would still suppress background noise\ncompared to the n = 1 system.\nThe revised version:\nLines 394-399: Experimental results demonstrate that the multi-channel (n = 2, n = 3)\ncorrelated source effectively suppresses noise relative to a direct rangefinding system (n = 1),\nwith greater noise suppression achieved as the number of channels increases and negligible\neffect on timing jitter.\nOverall, I would recommend the manuscript for publication as it demonstrates clear novelty\nand enhanced capabilities in quantum-inspired sensing.\nResponse: Thank you again for the highly positive comments. We have carefully addressed all\nthe questions and suggestions, which have helped us further refine the presentation and\nenhance the overall quality of the manuscript.\nReviewer #2 (Remarks to the Author):\nThis paper introduces a method for long-range, low-power optical rangefinding that leverages\nclassical laser systems to emulate the noise-resilience typically associated with quantum\nillumination. The approach exploits energy-time correlations generated via fiber-induced\nchromatic dispersion and electro-optic intensity modulation. The authors demonstrate sub-\nmillimeter ranging precision at distances exceeding 150 meters, all while operating under low\ntransmission power, with promising potential for scalability in both range and performance.\nHowever, in my view, the manuscript does not meet the significance threshold required for\npublication in Nature Communications. The novelty and impact of the work are limited when\nconsidered in the context of the current state of the field and the existing literature. A more\ntechnically focused journal may provide a more appropriate venue for this work.\nResponse:\nWe appreciate the reviewer’s feedback on the revised manuscript. However, we respectfully\ndisagree with the assessment regarding the novelty and impact of our work. The presented\nresults establish a new framework for quantum-inspired optical rangefinding, bridging\nquantum concepts with practical remote-sensing technologies. The main highlights are as\nfollows:\n1. Translation of quantum noise-reduction to a classical platform: Our quantum-\ninspired rangefinding system successfully translates the core noise-reduction\nmechanism of quantum lidar into a classical architecture, as verified through both\ntheoretical analysis and experimental validation. The noise-suppression effect is\npreserved and even enhanced by increasing the number of correlation channels, since\ndark-count noise remains largely unaffected by the addition of detectors. This\novercomes a key limitation of quantum rangefinding, which is restricted by an optimal\nchannel number.\n2. Significant improvement in source brightness and operational range: The source\nbrightness is increased by more than 60 dB compared to quantum sources, effectively\novercoming the range limitation that has so far confined demonstrations of noise-\nreduction advantages to short laboratory distances. Conventional quantum\nrangefinding typically operates over only a few metres, making it difficult to observe\nsignificant noise-resilience effects and limiting applicability in real-world conditions.\nOur approach removes this constraint, enabling practical deployment while\nmaintaining the noise-reduction advantages of quantum rangefinding. This represents\nthe first real-world demonstration of a quantum-inspired rangefinding system\noperating beyond laboratory settings.\n3. Demonstrated noise-resilience and robustness in real-world field trials: Successful\nfield trials under challenging environmental conditions, including ultra-low source\npower (48 µW), extremely high background (direct solar irradiation), long ranges (155\nm and 413 m), and a non-cooperative target (a building facade), demonstrate the\npractical noise-resilience and robustness of the proposed approach. Even under noise-\ndominated conditions (Fig. 5(d) and Fig. 6), our system can still retrieve range\ninformation from indistinguishable signal photons. Furthermore, its stable\nperformance under varying weather and solar illumination confirms its readiness for\nreal-world sensing applications.\nA detailed explanation and a comprehensive comparison with state-of-the-art have been\nprovided in Q2.7 and added to the Supplementary Information for clarity.\n-------------------------------------\nGeneral Comments:\n2.1 A central conceptual pillar of this work is its framing as \"quantum-inspired.\" The authors\nassert that the system inherits the noise-reduction benefits of quantum illumination —\nparticularly those coming from energy-time entangled photon pairs — without relying on\nactual entanglement. This distinction, however, is blurred throughout the manuscript.\n2.2 While it is true that structured correlations in time and frequency can mimic certain\nbehaviors seen in quantum systems, the correlation mechanism here is entirely\ndeterministic and rooted in classical signal engineering. The authors do not sufficiently\ndelineate the theoretical boundary between what is \"quantum-like\" in behavior and what\nis simply classical modulation and post-processing. Without any true non-classical light\nsource or statistics being involved, referring to the method as \"quantum-inspired\" risks\noverstatement.\n2.3 One important question that arises is whether the classical correlations employed here\nreplicate the information-theoretic and physical properties (such as resilience to loss,\nindistinguishability under thermal noise, and robustness against entropic decoherence)\nthat define true quantum illumination. The paper does not explore the theoretical limits\nof its system in comparison to, for instance, the optimal bounds predicted by quantum\nFisher information theory or Holevo capacities. As such, while the system borrows\nintuitions from quantum mechanics, it is not clear to what extent those benefits are\nfundamental versus incidental.\nResponse:\nWe thank the reviewer for raising these three comments regarding the distinction between\nquantum and quantum-inspired rangefinding, and we address them together below.\nFor remote detection under high transmission loss and strong background noise, the noise-\nreduction advantage observed in quantum rangefinding primarily arises from energy-time\ncorrelations across multiple frequency channels [1,2]. This correlation structure can persist\neven after entanglement is degraded, as discussed by Lloyd [2]. In this sense, the substantial\nenhancement in noise resilience associated with quantum illumination is rooted in the\ncorrelations themselves, rather than in the presence of entanglement. By contrast, the benefit\nuniquely attributable to entanglement has been shown to be limited to a 6 dB improvement\nand requires operation near the time-bandwidth limit with very low photon numbers per\ntiming window. This inherently limits the achievable source brightness by several orders of\nmagnitude compared to our system and therefore restricts quantum rangefinding to short\ndistances and highly reflective targets such as mirrors [3,4].\nOur work focuses on reproducing correlation-based enhancement using a classical optical\nsource suitable for realistic remote sensing scenarios, thereby achieving comparable noise\nsuppression without relying on entanglement. In our system, the source operates with a pulse\nduration exceeding 180 ps and a spectral bandwidth above 8 nm, corresponding to a time-\nbandwidth product much greater than unity. Therefore, the observed noise-reduction effect\narises entirely from energy-time correlations which is exactly the case in recent quantum\nrangefinder demonstrations [1], but in our case the correlations are classically engineered.\n2.1. In our terminology, quantum rangefinding refers to systems based on entangled-\nphoton sources, whereas quantum-inspired rangefinding refers to systems that\nemploy classically generated correlations. We have clarified this distinction explicitly\nin the Introduction.\n2.2. The term quantum-inspired is used intentionally to indicate that our approach is\nconceptually derived from the principles of quantum rangefinding. While the system\ndoes not employ non-classical light or entanglement, it retains the primary quantum-\nlike advantage of enhanced noise suppression, rather than quantum-specific\nbehaviour such as entanglement itself.\n2.3. Our objective is not to recreate entanglement in the source. Instead, we replicate the\nprimary operational noise-suppression benefit of quantum rangefinding by\nimplementing engineered classical correlations.\na. Resilience to loss: The developed source is more tolerant to high transmission\nloss than entangled sources, which aligns with our experimental results under\nvarying weather conditions, detection distances, and continuous 24-hour\noperation (Fig. 5, Fig. 6, and Fig. S2).\nb. Indistinguishability under thermal noise: In our experiments, the solar\nbackground exhibits near-Poissonian statistics because the detector time-\nbandwidth product is larger than unity (timing jitter ~150 ps and bandwidth ~\n10 nm). Under these detection conditions, our source is indistinguishable from\nthe solar background. Demonstrating thermal photon statistics would require\noperating at a time-bandwidth product near unity, which is not applicable to\nour system.\nc. Robustness against decoherence: Our system does not rely on phase\ncoherence (e.g., narrowband interference). As a result, the source remains\nrobust, and the original laser source could in principle be replaced with a\nthermal source without altering the performance.\nFor these reasons, analyses based on quantum Fisher information or Holevo\ncapacities are not informative, as the system operates entirely in the classical\nregime, and such bounds would not help optimize our approach.\nThe revised version:\nLines 108-115: This quantum-inspired rangefinding employs classically correlated optical\nsources while preserving most of the noise-reduction benefits of quantum rangefinding, which\nuses entangled-photon sources. To achieve the benefit of entanglement requires operating at\nthe time-bandwidth limit at low photon numbers per timing window, limiting operational\ndistance [3].\n[1] Frick, S., McMillan, A. & Rarity, J. Quantum rangefinding. Opt. Express 28, 37118-37128,\n(2020).\n[2] Lloyd, S. Enhanced Sensitivity of Photodetection via Quantum Illumination. Science 321,\n1463-1465, (2008).\n[3] Tan, S.-H. et al. Quantum Illumination with Gaussian States. Phys. Rev. Lett. 101, 253601,\n(2008).\n[4] Shapiro, J. H. & Lloyd, S. Quantum illumination versus coherent-state target detection. New\nJ. Phys. 11, 063045, (2009).\n2.4. The authors derive and experimentally validate a SNR model in which dark and\nbackground noise contributions are suppressed by increasing the number of independent\nenergy-time channels. While the data presented does support a trend of noise suppression,\nthe analytical model assumes ideal separation between channels and uncorrelated noise\nacross them. In real systems, however, factors such as timing jitter, spectral bleed, channel\ncrosstalk, and detector afterpulsing can erode the orthogonality and independence\nassumptions underpinning this model.\nResponse:\nWe thank the reviewer for raising this important point, which has been considered in the\nSupplementary Information (Lines 60–61):\n“𝜂 is the unbalance in channel power splitting with ∑𝑛 𝜂 = 𝑛,”\ni 𝑖=1 𝑖\nThe non-ideal separation between different channels has been incorporated into the SNR\nmodel through an imbalance parameter 𝜂 As shown in the detailed derivation, this non-ideal\ni.\nseparation does not affect the final SNR expression. Specifically, when substituting Eq. (S6)\ninto the signal term in Eq. (S5), we obtain\nn n N n\nS\n∑ C = ∑ 𝜂 𝜂 = N 𝜂 ∑ 𝜂 = N 𝜂\nSi n i S S S i S S\ni=1 i=1 i=1\nwhich demonstrates that the imbalance parameters cancel out when all channels are summed.\nFor uncorrelated noise, we initially did not include imbalance parameters, as their\ncontribution is negligible under strong background conditions. To make the model more\nrigorous, we have now introduced imbalance parameters for both background and dark count\nterms. This refinement aligns with our experimental results, where three channels with\ninherent imbalance showed consistent agreement with the theoretical model.\nRegarding the reviewer’s concern about practical non-idealities such as timing jitter, spectral\nbleed, channel crosstalk, and detector afterpulsing, we agree that maintaining channel\northogonality and independence is essential for preserving the generated energy-time\ncorrelations. These aspects are discussed and experimentally verified in our manuscript.\nSpecifically, we characterized the source in both the time and energy domains (Fig. 2), showing\nlow spectral bleed (>10dB isolation between channels). Furthermore, as shown in Fig. 4(c),\ninter-channel crosstalk contributes to the matrix elements 𝐶 where 𝑖≠𝑗, which partially\nij\nexplains the small discrepancy between experimental and theoretical results in Fig. 4(b). This\neffect can be further minimized by employing higher-precision spectral filters in the source or\nusing different methods for energy-time correlation generation.\nTo ensure completeness, we have refined the model by incorporating imbalance parameters\nfor the noise terms and added a discussion on addressing the influence of practical non-\nidealities.\nThe revised version\nSupplementary Information:\n1. Equation S8 and Lines 73-75: η is the channel unbalance in background counts\nub\nsplitting with ∑𝑛 𝜂 = 1;\nub=1 𝑢𝑏\n2. Equation S9 and Lines 88-90: η is the imbalance in the dark counts of different\nud\ndetectors related to the channel splitting, where ∑𝑛 𝜂 = 1;\nud=1 𝑢𝑑\n3. Lines 101-102: Upon summation over all channels, all imbalance parameters (η, η\ni ub\nand η ) are effectively cancelled.\nud\nMain manuscript:\n4. Lines 273-282: Uncorrelated counts (i ≠ j), which are primarily induced by the channel\ncrosstalk and time jitter, can be minimized by increasing the delay between adjacent\nchannels. As channel orthogonality and independence are crucial for the developed\nenergy-time correlations, low crosstalk and minimal timing jitter is required for\nsuccessful correlation generation, which can be further improved by employing higher-\nprecision spectral filters or different selection methods such as those discussed below\nand in Supplementary Section VII.\n2.5. I am a bit confused about the measurement. The experimental implementation uses three\nchannels; the authors extrapolate their model to predict substantial benefits at 80 channels\nusing commercial DWDM components. No information is provided about how increasing\nchannel count affects the complexity, calibration difficulty, or cross-channel synchronization\nof the system. Practical deployment of an 80-channel version would face significant scaling\nchallenges in terms of detector number, optical filtering precision, and FPGA control logic.\nThus, while the observed noise suppression is genuine within the limited configuration tested,\nthe scalability argument needs more substantiation — particularly given that real-world LIDAR\napplications demand robust and cost-efficient designs.\nResponse:\nWe thank the reviewer for raising the important issue of scalability. We fully agree that\npractical deployment requires careful consideration of system complexity, detector resources,\nfiltering precision, and synchronization. In principle, the scalability of our approach is\ntechnically feasible:\n1. The complexity and calibration challenges can be mitigated using integrated photonic\nplatforms [1,2], which provide compact, robust, and cost-effective solutions for increasing the\nnumber of channels. Once the chip design is finalized, the chip-based configuration offers\nstable alignment and straightforward operation.\n2. Detector requirements can be addressed by employing InGaAs detector arrays [3,4] or by\noperating in the near-infrared or visible regions, where high-performance silicon detectors are\nreadily available.\n3. Optical filtering precision can be achieved using mature commercial DWDM components\n[5,6], which routinely support 96 channels with low crosstalk (adjacent channel isolation >\n25dB) and stable spectral performance. Such filtering can also be realized using integrated\narrayed waveguide gratings [7], which provide compact and robust multiplexing solutions.\n4. The FPGA we use is an intermediate model that is cost effective (~£230) and can be used\nfor up to 16 channels. To increase channel number, we can synchronise multiple of these\ntogether [8] or opt for a higher specification model.\nThese clarifications highlight the realistic path toward robust, large-scale deployments of our\nquantum-inspired noise-suppression approach for rangefinding applications. Currently we are\ninvestigating an integrated 10-channel photonic chips on InP platform, which further\nsubstantiates the feasibility of scaling to high-channel-count, cost-efficient architectures. To\nclarify these aspects of scalability, we added a section in the supplementary information.\nThe revised version:\nManuscript Lines 311-315: Practical realization can be achieved through large-scale photonic\nintegration combined with off-chip commercial dense wavelength division multiplexing\n(DWDM) components and detector array technology (Supplementary Section VII).\nSupplementary Information (SI): A new SECTION VII SCALABILITY is added in the SI:\nConsidering scalability to a larger number of channels, integrated photonic platforms [1,2]\nrepresent a natural and practical path forward. They effectively address system complexity\nand calibration challenges while offering compact, robust, and cost-efficient solutions for\nmulti-channel optical architectures. Once the chip design is finalized, the integrated\nconfiguration provides intrinsically stable alignment and straightforward operation. Detector\nrequirements can be addressed by employing InGaAs detector arrays [3,4] or by operating in\nthe near-infrared or visible regions, where high-performance silicon detectors are readily\navailable. High-precision optical filtering can be achieved using mature commercial DWDM\ncomponents [5,6], which routinely support 96 channels with low crosstalk (adjacent channel\nisolation >25 dB) and excellent spectral stability. Alternatively, integrated arrayed waveguide\ngratings offer a compact and robust solution for scalable wavelength multiplexing [7]. Finally,\nthe FPGA we use is an intermediate model that is cost effective and can be used for up to 16\nchannels. To increase channel number, we can synchronise multiple of these together [8] or\nopt for a higher specification model, enabling parallel processing and straightforward system\nexpansion.\nRef:\n[1] Xu, X., Ren, G., Feleppa, T., et al. Self-calibrating programmable photonic integrated\ncircuits. Nat. Photon. 16, 595-602 (2022).\n[2] Pérez-López, D., Torrijos-Morán, L. Large-scale photonic processors and their\napplications. npj Nanophoton. 2, 32 (2025).\n[3] Dolphin J. A., Scowen R. O. E., Wells L. M., et al. Hybrid-Integrated InGaAs/InP SPAD Arrays\nfor Quantum Communications. arXiv preprint arXiv:2509.05134, (2025).\n[4] Tan, C. et al. Development of a near-infrared single-photon 3D imaging LiDAR based on\n64×64 InGaAs/InP array detector and Risley-prism scanner. Opt. Express 32, 7426-7447 (2024).\n[5] Ohara, T. et al. Over-1000-channel ultradense WDM transmission with supercontinuum\nmulticarrier source. J. Lightw. Technol. 24, 2311-2317, (2006).\n[6] Singh, S. & Kaler, R. S. Comparison of pre-, post- and symmetrical compensation for 96\nchannel DWDM system using PDCF and PSMF. Optik 124, 1808-1813, (2013).\n[7] Wang Z., Fang Z., Liu Z., et al. On‐Chip Arrayed Waveguide Grating Fabricated on Thin‐Film\nLithium Niobate. Adv. Photon. Res., 5(2), 2300228 (2024).\n[8] Xu Y., Rajagopala A. D., Fruitwala N., et al. Multi-FPGA Synchronization and Data\nCommunication for Quantum Control and Measurement. arXiv preprint arXiv:2506.09856,\n(2025).\n2.6. The authors report high range precision — down to ±48 µm — by performing Gaussian\nfits to the correlation peak in aggregated histograms. While this is technically accurate, it is\nimportant to distinguish between measurement precision (how consistently one can locate\nthe peak centroid) and resolution (how well two targets at different depths can be resolved).\nThe FWHM of the system’s impulse response, which defines depth resolution in practical\nterms, remains on the order of 25 mm.\nResponse:\nWe thank the reviewer for this comment, which aligns with the distinction we have made in\nthe manuscript. As correctly noted, measurement precision and resolution represent two\ndistinct aspects of system performance. The measurement precision reflects the statistical\nuncertainty in locating the centroid of the correlation peak, whereas the single-shot depth\nresolution is determined by the full width at half maximum (FWHM) of the three-channel\ncorrelation histogram. To clarify this distinction, we have revised the relevant sentences in the\nmanuscript as follows:\nThe revised version:\nLines 223-234: … centred at a distance of 154.81822(5) m. This fitting improves the\nmeasurement precision to ± 48 μm, representing the statistical uncertainty in locating the\npeak centroid and overcoming the limitations set by detector jitter. In contrast the single shot\ndepth resolution is determined by the full width at half maximum (FWHM) of combined the\nthree-channel histogram shown in Fig. 3(d), which is 25.7(1) mm. This value indicates how well\ntwo targets at different depths can be distinguished.\n2.7. One of the major weaknesses of the manuscript is the lack of systematic benchmarking\nagainst state-of-the-art classical technologies. The only substantive comparisons are made\nwith quantum rangefinding systems based on SPDC, which are inherently limited by low\nbrightness and high experimental fragility, especially in daylight.\nThe high-performance LIDAR systems based on time-correlated single-photon counting,\nfrequency-modulated continuous wave principles, and pulsed illumination with GHz detection\nbandwidths have made significant progress in long-range detection, noise rejection, and\ncovert operation. Many of these use sophisticated coding schemes and multi-channel\napproaches not dissimilar in spirit to what is proposed here.\nResponse:\nWe thank the reviewer for this valuable comment regarding benchmarking. In our work, we\nhave included comparisons with both classical and quantum rangefinding systems. For the\nclassical case, as also noted by the first reviewer, we defined the direct rangefinding\nconfiguration as the single-channel case (n = 1). This provides a fair and controlled benchmark,\nas all experimental conditions remain identical except for the number of channels. The\nobserved improvement in noise suppression with increasing channel number (n = 2 and 3) not\nonly validates our theoretical model but also demonstrates a direct and practical performance\ngain relative to classical systems. For quantum rangefinding, comparisons have been made\nwith previously reported systems based on SPDC sources, as recognized by the second\nreviewer.\nAdditionally, we have included a comprehensive state-of-the-art performance comparison\nand detailed discussion in the Supplementary Information. This survey spans quantum\nrangefinding [1], Chaotic-QFC LiDAR (Quantum-inspired LiDAR) [2], High Performance Single\nPhoton LiDAR [3-6], GHz-SPAD LiDAR [7], and FMCW LiDAR [8,9]. The comparison table\nevaluates key performance metrics, including source average power, detection range,\ndetected target, collection aperture, detector type, and background noise, enabling an\nassessment of long-range capability under operationally critical conditions.\nRegarding “sophisticated coding schemes and multi-channel approaches” mentioned by\nreviewer, sophisticated coding schemes [3,10] have traditionally been employed to extend the\nambiguity range imposed by a fixed repetition rate. Multi-channel systems [6,11] have\nprimarily been reported in spectral-scanning applications with grating, where wavelength\nchannels are distributed spatially rather than temporally onto the illuminated target, as\nimplemented in this work. Although the corresponding experimental configurations may\nappear superficially similar, the underlying principles, intended applications, and resulting\nperformance characteristics differ substantially from those reported previously. Crucially, no\nprior system has combined both architectures with wavelength-time coding (i.e., energy-time\ncorrelation) to achieve noise reduction. This integration represents a key innovation of the\npresent work, enabling long-range, low-power operation under strong and realistic\nbackground illumination, where capabilities not demonstrated in earlier studies.\nThe revised version:\nSupplementary Information: Section VI. STATE-OF-THE-ART COMPARISON\nA comprehensive comparison of state-of-the-art performance metrics is provided in Table S1,\ncovering quantum rangefinding [1], chaotic quantum frequency conversion (chaotic-QFC,\nquantum-inspired) Light Detection and Ranging (LiDAR) [2], high-performance single-photon\nLiDAR systems [3–6], Gigahertz single-photon avalanche diode (GHz-SPAD) LiDAR [7], and\nfrequency-modulated continuous-wave (FMCW) LiDAR technologies [8,9]. Compared with\nquantum rangefinding demonstrations [1], the source brightness employed here is\nsubstantially higher yet remains within the covert-illumination limits established in the covert-\nanalysis (Supplementary Information Section V). This enables long-distance operation without\nexceeding covert thresholds. By contrast, most classical LiDAR systems use optical powers > 1\nmW, at least 20 times higher than in this work, and therefore operate outside the covert\nregime. Achieving ranges beyond 1 km with a low-reflective target typically requires either\nmore than Watt illumination or highly sensitive, cryogenic detectors such as superconducting\nnanowire single-photon detectors (SNSPDs) in the reported systems. This is either not good\nfor brightness covertness or compact detection system. It is worth noting that our approach\ncan readily support longer distance through increased optical power or extended integration\ntimes.\nOur experimental conditions also impose more stringent loss factors than those used in many\nprevious field demonstrations. Measurements were performed using an older building with\nan irregular, low-reflectivity facade, introducing significant surface-scattering loss. In contrast,\nmany long-range studies use high-reflectivity targets, where losses are dominated primarily\nby beam divergence. The receiver optics in our system consist of a compact 48 mm aperture,\noffering a portable and practical collection system for deployment. For detection, we use\nsingle-photon avalanche diodes (SPADs), which offer an effective balance of sensitivity,\nrobustness, and cost. This contrasts with homodyne-based receivers, which, despite their\nsensitivity, are mechanically fragile and challenging to deploy outside the laboratory, and with\nSNSPDs, which are costly and require continuous cryogenic cooling.\nThe background illumination conditions in our measurements further represent a demanding\nand realistic outdoor scenario. As shown in Fig. 5(d), the target building is directly exposed to\nsunlight, resulting in a solar background level nearly three orders of magnitude higher than\nthe transmitted power, as quantified in the covertness analysis in Section V. Many reported\nstudies either simulate ambient noise in controlled laboratory settings or conduct\nmeasurements under standard daylight conditions without quantifying the background level.\nThe results presented here therefore demonstrate system performance under\noverwhelmingly strong and realistic background noise levels encountered in practice.\nIn conclusion, our field trial employed an ultra-low-power (48 µW) source to detect a remote\ntarget directly illuminated by sunlight, representing an extremely high-background scenario.\nEven in these noise-dominated conditions, where the ambient background exceeded the\nsignal by nearly three orders of magnitude, the system successfully recovered signal photons.\nThese results highlight the practical robustness and exceptional noise tolerance of the\napproach, demonstrating its suitability for real-world deployment.\nTable S1 State-of-the-Art Performance Comparison for Quantum and Classical Lidar System\nSystem Avg. Tx Detection Detected Collection Detector Background Noise\nPower Range Target Aperture Type\nQuantum-inspired Rangefinding 48 µW 413 m Building 48 mm SMF-coupled SPAD Direct solar irradiation on target\n(This work) (Background ≈ 103 × signal)\nQuantum Rangefinding [1] pW-scale 3 m (lab) Corner-cube 48 mm Si APD LED-simulated\nChaotic-QFC LiDAR 50 mW 4 m (lab) Indoor 50.8 mm Balanced Homodyne Simulated by amplified\n(Quantum-inspired LiDAR) [2] quadcopter Detection spontaneous emission (ASE)\nnoise\nSNSPD Single Photon LiDAR [3] 2.9 mW 1 km Comms mast 254 mm Single-mode-fibre (SMF) Daylight\n(metal frame) coupled SNSPD\nSatellite Single-Photon LiDAR [4] 15 W 935.9 km Retroreflective 280 mm SMF-coupled SPAD Night\nsatellite\nSingle Photon LiDAR with 64x64 2.5 W 5.7 km Building 50 mm 64×64 InGaAs/InP SPAD Daylight\nSPAD Array [5] array\nHigh-Repetition-Rate Single 200 mW 340 m DJI mini3 40 mm Multi-mode-fibre (MMF) Not stated\nPhoton LiDAR [6] coupled SNSPD\nAirborne GHz-SPAD LiDAR [7] 107 mW 620 m Ground 15.3 mm MMF-coupled SPAD Morning\n(Background ≈ 30× signal)\nOPA-based FMCW LiDAR [8] ≤ 40 W 2 km Building 350 mm Free space InGaAs APD Night\nLong-range FMCW LiDAR [9] 1 W CW 3 km Houses 20 mm Coherent balanced Clear air\nphotodiodes\nRef:\n[1] Frick, S., McMillan, A. & Rarity, J. Quantum rangefinding. Opt. Express 28, 37118-37128,\n(2020).\n[2] Liu, H., Qin, C., Papangelakis, G., Iu, M. L. & Helmy, A. S. Compact all-fiber quantum-inspired\nLiDAR with over 100 dB noise rejection and single photon sensitivity. Nat. Commun. 14, 5344,\n(2023).\n[3] McCarthy, A. et al. High-resolution long-distance depth imaging LiDAR with ultra-low\ntiming jitter superconducting nanowire single-photon detectors. Optica 12, 168-177, 77\n(2025).\n[4] Li, Y. et al. Compact single-photon LiDAR for satellite laser ranging. Opt. Express 33, 40876-\n40890, (2025).\n[5] Tan, C. et al. Development of a near-infrared single-photon 3D imaging LiDAR based on\n64×64 InGaAs/InP array detector and Risley-prism scanner. Opt. Express 32, 7426-7447, (2024).\n[6] Zhang, W. et al. Sensitive micro UAV detection based on a high-repetition-rate single-\nphoton LiDAR. Opt. Express 33, 18102-18111, (2025).\n[7] Shen, G. et al. High-speed airborne single-photon LiDAR with GHz-gated single-photon\ndetector at 1550 nm. Opt. Laser Technol. 141, 107109, (2021).\n[8] Wu, Y. et al. Multi-beam optical phase array for long-range LiDAR and free-space data\ncommunication. Opt. Laser Technol. 151, 108027, (2022).\n[9] Feneyrou, P., Martin, A., Dolfi, D. & Payot, E. 3D imaging with large range dynamics and\nsimultaneous accurate speed measurement. Appl. Opt. 63, 5387-5394, (2024).\n[10] Krichel, N. J., McCarthy, A. & Buller, G. S. Resolving range ambiguity in a photon counting\ndepth imager operating at kilometer distances. Opt. Express 18, 9192-9206 (2010).\n[11] Jiang, Y., Karpf, S. & Jalali, B. Time-stretch LiDAR as a spectrally scanned time-of-flight\nranging camera. Nat. Photonics. 14, 14-18, (2020).\n2.8. The paper makes a compelling case that the use of ultra-low transmission power and\npseudo-random coding enables covert rangefinding. While the low-power operation is\nevident, the claim of covertness is only speculative. No data or analysis is provided to show\nhow detectable (or undetectable) this system would be in practice against standard detection\ntools like optical time-domain reflectometers or RF/optical side-channel analyzers.\nResponse:\nWe thank the reviewer for raising the concern regarding the claim of covertness.\nThe covertness we are considering here is the inability of the target to be able to distinguish\nwhether the transmitter is on or off (i.e., are they being ranged). Our system is promising for\nthis, as the intensity of the transmitter light at the target is less than the intensity of the solar\nbackground. A tighter constraint on covertness is that the number of photons that are\ncollected at the target in a particular area is less than the fluctuation in photon number from\nthe solar background in the same area. Our system achieves this criterion for the highest solar\nbackground levels seen in full daylight with the detailed discussion added in Supplementary\nInformation. For other times of day, we can modify the average number of photons\ntransmitted to be covert, but at night in the absence of background this is difficult to achieve.\nAs our receiver has a low field of view due to single mode fibre collection, it will only receive\nscattered light from our transmitter and solar background from the target surface with a\ncomparable illumination area. We see in Figs. 5(h) and 6(b), that the optical signal peaks are\nfully obscured by the background noise level, demonstrating that the emitted probe remains\nindistinguishable from ambient background fluctuations on the receiver side.\nWith respect to the detection tools mentioned, we assume that the reviewer is referring to\nmethods for the target to either detect modulated optical signals from the transmitter or use\ntechniques to discern that the transceiver system is present. Here we have not considered\nconcealing the transceiver, but this could be camouflaged. We consider covertness to be\nknowing whether the transceiver is operating or not. In terms of observing the RF modulation\nof the transmitter, this could be possible with the current system, but true random channel\nsequences and randomized timing modulation [1], which enable temporal-domain\nconcealment (mentioned on Lines 451-453 of the main manuscript). Spectral concealment can\nbe further enhanced by extending the current 60 nm broadband operation to a wider spectral\nrange through additional channels. From a photon-statistics perspective, the thermal\ndistribution can be mimicked by using a thermal source or coherent pulses with randomly\nchosen intensities [2].\nFinally, we emphasize that covertness is not the main focus of the present work but is\ndiscussed in the context of highlighting the potential of our approach for future covert\nrangefinding applications. A systematic analysis of covert performance under various\noperational conditions will be the subject of our forthcoming study. Accordingly, we have\nrevised the relevant discussion and added appropriate references in the revised manuscript.\nThe revised version:\nLines 441-464: For instance, in terms of brightness, which is the fundamental prerequisite for\nall measurements, the transmission power is set to a low level of 48 μW, with pulse\ncompression applied to obscure the generated correlations. As shown in Figs. 5(h) and Fig.\n6(b), the optical signal peaks are fully concealed within the ambient background noise, with\nthe solar background level nearly three orders of magnitude higher than the signal power, as\nquantified in Supplementary Section V. To achieve fully covert operation, the unique signature\nof the laser source requires further manipulation. For example, the detectable repetition rate\ncan be randomized by introducing random time delays or being triggered by a true random\nsequence derived from, for example, shot noise [1], spontaneous Raman scattering [3],\nchaos laser [4], or a quantum random number generator [5]. Channel indices can also be encoded\nusing a true random sequence. Spectral concealment can be further enhanced by extending\nthe current 60 nm broadband operation to a wider spectral range through additional channels.\nMoreover, the laser pulses can be randomly intensity-modulated [2] or replaced with a\ntriggered thermal source to replicate the super-Poissonian statistics of solar background.\nSupplementary Information: add “Section V. Covertness in Brightness”:\nThe covertness we are considering is the inability of the target to be able to distinguish\nwhether the transmitter is on or off (i.e., are they being ranged). Our system is promising for\nthis, as the intensity of the transmitter light at the target is less than the intensity of the solar\nbackground. A tighter constraint on covertness is that the number of photons that are\ncollected at the target in a particular area is less than the fluctuation in photon number from\nthe solar background in the same area. In this work, the average source power is 48 µW,\nproducing an illumination spot of approximately 86.7 mm in diameter on the target building\n(WMB). This corresponds to an irradiance of 0.00813 W/m². By comparison, the solar\nbackground irradiance around 1550 nm wavelength is approximately 0.25 W/m²/nm.\nAssuming the target selects the same 30 nm bandwidth used in our experiment, the effective\nsolar background irradiance is 7.5 W/m², which is three orders of magnitude higher than the\nsource. While our source power is not comparable to shot-noise fluctuations of the solar\nbackground, environmental fluctuations in the solar background are expected to exceed 1%\non short time scales and are often found to be over 10% [6]. Thus, our system satisfies this\ntighter covertness criterion, with the transmitted signal level more than 10 times lower than\nthe background fluctuations.\nRef:\n[1] Liu, B., Yu, Y., Chen, Z. & Han, W. True random coded photon counting Lidar. Opto-Electron.\nAdv. 3, 190044 (2020).\n[2] Brougham, T., Samantaray, N. & Jeffers, J. Using random coherent states to mimic quantum\nillumination. Phys. Rev. A 108, 052404, (2023).\n[3] Collins, M. J. et al. Random number generation from spontaneous Raman scattering. Appl.\nPhys. Lett. 107, 141112 (2015).\n[4] Hu, Z. et al. Chaos single photon LIDAR and the ranging performance analysis based on\nMonte Carlo simulation. Opt. Express 30, 41658-41670, (2022).\n[5] Zhang, Y. et al. A simple low-latency real-time certifiable quantum random number\ngenerator. Nat. Commun. 12, 1056, (2021).\n[6] Kreuwel, F. D. M. et al. Analysis of high frequency photovoltaic solar energy fluctuations,\nSol. Energy, 206, 381-389 (2020).\n2.9. The experimental demonstration is undoubtedly impressive, particularly the ability to\nmeasure distances with sub-mm accuracy across a 150–400 meter baseline in varying weather\nand lighting conditions. However, the paper will benefit from additional discussion of\nenvironmental robustness — for example, whether alignment drift, thermal effects, or fiber\nmovement degrade performance. Additionally, long-term stability tests and repeatability of\nprecision across independent trials are not discussed.\nResponse:\nWe thank the reviewer for the positive assessment of our experimental results and for the\nvaluable comment regarding environmental robustness. We have addressed all related\naspects in Supplementary Information Section IV, including the effects of alignment drift,\nthermal variations, and fiber movement on system performance, as well as long-term stability\ntests and the repeatability of measurement precision across independent trials.\nTo summarize, our results demonstrate that the system exhibits strong robustness during day-\nto-day field operation under various environmental conditions, including nighttime, sunny,\ncloudy, and rainy periods. This performance is enabled by the noise-reduction capability of\nthe developed source, which remains effective, and even more pronounced, under high\ntransmission loss and strong background illumination. As a result, performance degradation\ndue to factors such as alignment drift or outdoor fiber movement is negligible. All optical\ncomponents and connecting fibers are securely mounted and show no noticeable influence\non the ranging results.\nContinuous 24-hour testing further confirms the system’s stability and repeatability, as shown\nin Fig. S2. Thermal effects are clearly observable; while these can be mitigated through\nimproved thermal insulation, the inherent temperature sensitivity can also serve as a useful\nfeature for tracking ambient temperature variations. Importantly, the measured distance\nreturns to its original value during the following night, demonstrating strong measurement\nconsistency under fluctuating real-world conditions. A minor periodic fluctuation is observed,\nwhich is attributed to the FPGA’s internal temperature changing and can be reduced with\ndedicated thermal control.\nThese findings clearly indicate that the proposed system is inherently robust and well suited\nfor practical field deployment.\nThe revised version:\nSupplementary Information\nSection IV. Long-term Stability and Environmental Robustness\nConsidering long-term stability and repeatability, a systematic evaluation of environmental\nrobustness was performed through continuous 24-hour field testing. As shown in Fig. S2, the\nmeasured distance was recorded from midnight to the following midnight with an integration\ntime of 0.1 s and a sampling interval of 6 min. Measurement repeatability was determined\nfrom 60 measurements acquired with a 1-second interval, allowing the calculation of the error\nbars in the plot.\nA range fluctuation of approximately 11 mm (corresponding to a ~73 ps time drift) with a\nperiod of ~24 min was observed, which is likely caused by temperature-dependent delay and\nphase variations in the Zynq-7000 FPGA’s internal clocking and routing circuitry. In future work,\nthis will be addressed by using closed-loop temperature control of the FPGA. The overall long-\nterm range tendency is attributed to thermal effects and follows the recorded temperature\nevolution, as indicated by the average temperature variation trace (red line in Fig. S2 [1]).\nWhile such effects can be mitigated using improved thermal isolation on fibre cable, the\ninherent temperature sensitivity may also serve as a useful feature for tracking environmental\ntemperature changes. Importantly, the measured distance returns to its initial value at night,\nconfirming strong measurement consistency under fluctuating ambient conditions.\nAdditional factors that may influence system stability are further analysed and discussed\nbelow:\n1. Alignment stability: The optical alignment remained stable throughout day-to-day\nfield measurements and was unaffected by changes in lighting or weather. As shown\nin Fig. S2, all optical components are securely fixed on a rigid mounting platform, and\nthe transmitter and receiver share the same multi-axis rotation stage, ensuring\nstructural stability. In addition, the use of Lambertian backscattering relaxes alignment\nconstraints, as the detection is less sensitive to variations in target surface angle.\n2. Thermal effects: The fibres in the source and detection modules were housed in a\ntemperature-controlled laboratory environment, where temperature-induced\nvariations are minimal. Only the 300 m outdoor telecom fibre linking the laboratory\nand the balcony was exposed to environmental temperature changes. As shown in Fig.\nS2, the range change from 3 a.m. to 3 p.m. is approximately 20 mm, corresponding to\na 133.3 ps timing difference and an 11.4 K temperature change with a thermal\ncoefficient of 39 ps·km⁻¹·K⁻¹ [2]. The hourly average temperature data (red line) from\nthe Bristol Airport weather station [1] indicates a temperature variation of about 4 K\n(°C) over the same period. The discrepancy from the inferred 11.4 K may arise from\nlocal temperature differences between the airport and the city-center university\nbuildings. Nevertheless, as shown in Fig. S2, the observed range variation closely\nfollows the general temperature trend recorded around Bristol Airport. The associated\nattenuation remains below 0.05 dB [3] for temperatures between -60 °C and 85 °C,\nwhich is negligible for this system, especially as the noise-reduction performance\nremains effective, and even more pronounced, under high transmission loss conditions.\n3. Fiber movement: The system is inherently resilient to fiber-induced disturbances. The\nnoise-suppression performance remains strong and becomes even more pronounced,\nunder high-loss and high-background conditions. Moreover, phase and polarization\nfluctuations do not impact the field trial, as the system does not rely on interferometric\nsensitivity. Consequently, bending losses, power variations, and external perturbations\nintroduce no observable degradation during field trials.\nFig. S2 | 24-hour continuous field testing. Detected range (Blue) and hourly average\ntemperature (Red) as a function of time over the 24-hour measurement period, from midnight\nto the following midnight. The range is measured with an integration time of 0.1 s. Error bars\nrepresent the standard deviation of 60 independent range measurements acquired within\neach 1-second time window. The range is found at a sampling interval of 6 min. The hourly\naverage temperature data were recorded from the Bristol Airport weather station from\nWeatherSpark.com [1]. Nighttime and civil twilight are indicated by shaded background\noverlays.\nRef:\n[1] Data downloaded from https://weatherspark.com/h/d/39587/2024/10/12/Historical-\nWeather-on-Saturday-October-12-2024-in-Bristol-United-Kingdom\n[2] Slavík R., Marra G., Fokoua E. N., et al. Ultralow thermal sensitivity of phase and\npropagation delay in hollow core optical fibres. Sci. Rep. 5(1), 15447 (2015).\n[3]PDF available at\nhttps://lewinb.net/posts/12_what_every_programmer_should_know_about_optical_fiber/P\nI-1470-AEN.pdf."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have satisfactorily replied to my questions and comments", "reviewer_2": "The authors have addressed my questions and revised the manuscript appropriately. I therefore recommend the publication\nof the work in Nature Communications."}, "author_response": ""}]

Decision letter