Patent Description:
Quantum cryptography or quantum key distribution (QKD) are known to ensure a secured point-to-point communication. The security provided by quantum key distribution (QKD) protocols is harnessed to the laws of quantum physics and thus independent of all future advances of algorithm or computational power. The most used quantum key distribution (QKD) protocols are the prepare and measure BB84 protocol based on a single photon source or the E91 protocol based on an entangled photon source. The key generation is based in the most cases on the polarization of single photons or entangled photon pair.

To perform a polarization measurement passive and active systems are known. In passive systems an optical element, for example a beam splitter is used to split up the beam path and thus enable the measurement in two different bases by additional polarization elements, for example polarizer and detectors. The disadvantage of a passive system is the large number of optical components and the high losses in the system in order to measure in two mutually unbiased bases, as required by the most quantum key distribution (QKD) protocols.

In active systems the base in which to measure is determined by an active polarization influencing element, for example an electro optical modulator switching between the two bases to be measured followed by a polarization element, for example polarizer and detectors. The disadvantage of an active system is the higher loss of the polarization influencing element and the necessity to use additional elements in order to enable a random base choice, as required by the most quantum key distribution (QKD) protocols.

<CIT> discloses a polarization analysis module and method for polarization analysis.

It is an object of the present invention to provide an improved and low loss passive polarization analysis module and method thereof.

According to the present invention, a polarization analysis module is provided according to claim <NUM>.

The inventive polarization analysis module, preferably for quantum communication, quantum cryptography, and/or quantum key distribution (QKD), comprises a first and a second diffraction element, a wave-plate, and at least four single photon detectors, in order to enable a polarization analysis of single photons in two mutually unbiased bases and two orthogonal states per base. According to the invention, the first and second diffraction elements are polarization-sensitive first and second dielectric metastructure gratings, and the wave-plate is arranged between the first and second dielectric metastructure grating, and at least two detectors are arranged in diffraction paths of the first diffraction element, and at least two detectors are arranged in diffraction paths of the second diffraction element.

The object is further achieved by a method for polarization analysis according to claim <NUM>.

The inventive method for polarization analysis of single photons, preferably for quantum communication, quantum cryptography, and/or quantum key distribution (QKD), is realized in a first base and a second base and two orthogonal states per base, whereby the first and the second bases are two mutually unbiased bases, whereby a first single photon possesses a polarization in one of the two orthogonal states of the first base and a second single photon possesses a polarization in one of the two orthogonal states of the second base.

According to the invention, a first dielectric metastructure grating transmits or diffracts the first and/or second single photon randomly, and.

An advantage of the inventive polarization analysis module and the inventive method for polarization analysis is the use of two polarization-sensitive dielectric metastructure gratings and the analysis by diffraction, leading to a low loss and high contrast polarization measurement of single photons.

Another advantage of the inventive polarization analyzer and the method is the random polarization-insensitive transmission or polarization-dependent diffraction in the first dielectric metastructure grating and the polarization dependent diffraction by the second dielectric metastructure grating. By the random transmission a random choice of the base in which to measure is realized as required by quantum key distribution (QKD) protocols. In addition, the first dielectric metastructure grating replaces multiple optical elements, as this one dielectric metastructure grating fulfills a polarization dependent diffraction and the function of a random choice of the base.

An advantage of the inventive module and method by the use of two dielectric metastructure gratings is, that gratings with small period can be used leading to a better resolution in other degrees of freedom, for example a possible wavelength dependent separation in addition to the polarization measurement.

With certainty means here, the detection of the polarization of the first single photon in one of the two orthogonal states of the first base by <NUM>% when the first single photon is diffracted on the first dielectric metastructure grating, assuming a detection efficiency of the detector with <NUM>%. If the first single photon is transmitted through the first dielectric metastructure grating, the polarization of the first photon is determined by the second dielectric metastructure grating in one of the two orthogonal states of the second base with uncertainty, that means with a random outcome of <NUM>% in each diffraction path of the second dielectric metastructure grating.

This also applies for the second photon; With certainty means here, the detection of the polarization of the second single photon in one of the two orthogonal states of the second base by <NUM>% when the second single photon is diffracted on the second dielectric metastructure grating, assuming a detection efficiency of the detector with <NUM>%. If the second single photon is diffracted by the first dielectric metastructure grating, the polarization of the second photon is determined by the first dielectric metastructure grating in one of the two orthogonal states of the first base with uncertainty, that means with a random outcome of <NUM>% in each diffraction path of the first dielectric metastructure grating.

Diffraction by the first and/or the second polarization-sensitive dielectric metastructure grating means here, an angle dependent polarization diffraction.

A polarization-dependent diffraction at the first polarization-sensitive dielectric metastructure grating can be described by the diffraction angle β with <MAT> whereby α denotes the angle of incidence; λ denotes the wavelength; P denotes the period of the first metastructure grating; m denotes the used or selected diffraction order of the first metastructure grating. γ corresponds to the projection of the single photon state of polarization to the first orthogonal state of the first mutually unbiased base of the metastructure grating.

A polarization-dependent diffraction at the second polarization-sensitive dielectric metastructure grating can be described by the diffraction angle β with <MAT> whereby α denotes the angle of incidence; λ denotes the wavelength; P denotes the period of the first metastructure grating; m denotes the used or selected diffraction order of the second metastructure grating. γ corresponds to the projection of the single photon state of polarization to the first orthogonal state of the second mutually unbiased base of the metastructure grating.

In a preferred embodiment, the inventive polarization analysis module and/or the method for polarization analysis is used for polarization analysis for multiple first single photons and multiple second single photons, preferably one after the other, more preferably in random order. In a preferred embodiment, the first and/or second single photon is a single photon or a single photon from a polarization entangled photon pair, preferably a signal photon or an idler photon.

In a preferred embodiment, the first dielectric metastructure grating transmits the first and/or second single photon with <NUM>% probability or diffracts the first and/or second single photon with <NUM>% probability. In a preferred embodiment, the second dielectric metastructure grating diffracts the first and/or second single photon, preferably with <NUM>%. In a preferred embodiment, the first dielectric metastructure grating is a polarization-insensitive beam splitting element, preferably a <NUM>/<NUM> beam splitter, and a polarization-sensitive diffraction element and the second dielectric metastructure grating is a polarization-sensitive diffraction element.

In a preferred embodiment, the first dielectric metastructure grating performs the measurement of the first single photon in the first mutually unbiased base. In a preferred embodiment, the wave-plate and the second dielectric metastructure grating perform the measurement of the second single photon in the second mutually unbiased base.

In a preferred embodiment, the first dielectric metastructure grating enables the measurement of the single photon in the two orthogonal states of the fist mutually unbiased base. In a preferred embodiment, the first orthogonal state of the first mutually unbiased base is resolved by the diffraction of the first single photon in the +<NUM>st diffraction order of the first dielectric metastructure grating. In a preferred embodiment, the second orthogonal state of the first mutually unbiased base is resolved by the diffraction of the first single photon in the -<NUM>st diffraction order of the first dielectric metastructure grating.

In a preferred embodiment, the second dielectric metastructure grating and the wave-plate enables the measurement of the single photon in the two orthogonal states of the second mutually unbiased base. In a preferred embodiment, the first orthogonal state of the second mutually unbiased base is resolved by the diffraction of the second single photon in the +<NUM>st diffraction order of the second dielectric metastructure grating. In a preferred embodiment, the second orthogonal state of the second mutually unbiased base is resolved by the diffraction of the second single photon in the -<NUM>st diffraction order of the second dielectric metastructure grating.

For a quantum key distribution protocol in most cases the source of the single photons and the receiver, or the two receivers of single photons have to agree on two mutually unbiased bases to generate a key. The measurement is performed in two orthogonal states per base at each receiver. As a non-exclusive example, the two mutually unbiased bases can be two out of the three H/V base, +/- base, and L/R base, with H denotes linear horizontal polarization, V denotes linear horizontal polarization, + denotes linear <NUM>° polarization, - denotes linear <NUM>° polarization, L denotes left-hand circular polarization, R denotes right-hand circular polarization. It is also possible to realize a quantum key distribution protocol with two others, preferably elliptically polarized mutually unbiased bases and their orthogonal states.

In a preferred embodiment, the first and/or second dielectric metastructure grating diffracts single photons in the first base, preferably circular polarization, in the ±<NUM>st diffraction order. In a preferred embodiment, the second dielectric metastructure grating diffracts by the use of the wave-plate in front of the second dielectric metastructure grating single photons in the second base, preferably linear polarization, in the ±<NUM>st diffraction order.

In a preferred embodiment, a polarization rotator is arranged in front of the first dielectric metastructure grating. The polarization rotator allows a rotation of the polarization states depending on its setting from any point to any point on the Poincaré-sphere. In a preferred embodiment, the polarization rotator in front of the first dielectric metastructure grating set the bases of the first dielectric metastructure grating. The advantage of this embodiment is the independent and flexible choice of the two mutually biased bases in the setup by the polarization rotator and the wave-plate. By these two elements all possible mutually unbiased bases on the Poincaré sphere can be detected by the module and the method.

In a preferred embodiment, the polarization rotator is a quarter-wave-plate, and/or a half-wave-plate, and/or a soleil Babinet compensator, or a combination of a first quarter wave-plate, a half wave-plate, and a second quarter-wave-plate.

In a preferred embodiment, the wave-plate and/or the polarization rotator introduce a unitary (coherence conserving) transformation of the polarization of the first and/or second single photon. This can be realized by birefringent elements and can be understood as a rotation of the polarization states on the Poincaré-sphere about a particular axis.

In a preferred embodiment, the wave-plate between the first and the second dielectric metastructure grating is a quarter wave-plate, preferably at <NUM>° in order to diffract the second single photons in the H/V base.

In a preferred embodiment, the wave-plate between the first and the second dielectric metastructure grating is a quarter wave-plate, preferably at <NUM>° in order to diffract the second single photons in the +/- base.

In a preferred embodiment, the wave-plate and/or the polarization rotation element acts as an element rotating the polarization. The rotation of the polarization is a unitary transformation of the polarization, that means only a transformation but not a measurement.

In a preferred embodiment, the wave-plate and the second dielectric metastructure grating are arranged in the transmission path, preferably <NUM>th order diffraction path, of the first dielectric metastructure grating behind the first dielectric metastructure grating. <NUM>th order diffraction path means here that the photon is transmitted without diffraction.

In a preferred embodiment, the at least two detectors are arranged in two selected diffraction paths of the first diffraction element, preferably two diffraction paths of orthogonal polarization.

In a preferred embodiment, the at least two detectors behind the first and/or second dielectric metastructure grating are arranged in the ±<NUM>st order diffraction path of the first and/or second dielectric metastructure grating, and/or a higher order diffraction path.

In a preferred embodiment, the first and/or second dielectric metastructure grating split each diffraction path up by one or more additional degrees of freedom. In a preferred embodiment, the additional degree of freedom is the wavelength of the single photon, and/or orbital angular momentum.

In a preferred embodiment, in each additional degree of freedom diffraction path a detector is arranged, in order to detect the first and/or second single photon in a specific diffraction path and with a specific additional degree of freedom.

Embodiment with additional degree of freedom allows a polarization analyzation of the single photon and an analyzation in the additional degree of freedom of this single photon at the same time. This is realized by the polarization dependent diffraction on the first and/or second dielectric metastructure grating and an additional angle of diffraction introduced by the additional degree of freedom.

This leads for example to an additional division of the ±<NUM>st order diffraction paths into several wavelength or orbital angular momentum dependent ±<NUM>st order diffraction paths. An advantage of this embodiment is the analysis of different degrees of freedom in one setup and by one method at the same time. This could be used to increase the key generation rate by using a second degree of freedom and additional detectors to overcome the limit of the key generation rate by only one detector. The key generation rate with one detector is for example limited by the death time of the detector.

Dielectric metastructure grating means here a two-dimensional periodic metastructure of dielectric nano-structures. The two-dimensional lattice structure of the nano-structures can be rectangular, hexagonal, or quasiperiodic. The nano-structures can be dielectric cuboids, nanobeams, elliptical or rectangular air-holes, V-antennas, or any other laterally anisotropic structures.

In a preferred embodiment, the dielectric nano-structures are dimension- or orientation-varying nanoposts, orientation-varying nanobeams, double rectangular resonators with varying spacings and/or widths, and/or rectangular mesh.

In a preferred embodiment, the first and/or second dielectric metastructure grating comprises an orientation varying and/or a dimension varying metastructure.

For the dimension-varying metastructures, the sizes or shapes of the metastructures are spatial-dependent, and determine the local optical phase. The shape of the metastructures affects the resonance frequencies.

For the orientation varying metastructure, only the orientation of the metastructures is varied, whereby this is also known as Pancharatnam-Berry (PB) phase. With the Pancharatnam-Berry (PB) phase design, the local optical phase is completely controlled by the orientation of the metastructures with uniform size and shape.

In a preferred embodiment, the first and/or second dielectric metastructure grating comprises a planar Pancharatnam-Berry phase structure in order to diffract the photons in addition to the polarization on their orbital angular momentum.

In a preferred embodiment, the first and/or second dielectric metastructure grating has a size of at least <NUM> x <NUM>, preferably at least <NUM> x <NUM>, more preferably at least <NUM> x <NUM>.

In a preferred embodiment, the first and/or second dielectric metastructure grating has a period comprising more than <NUM> nano-structures.

In a preferred embodiment, the nano-structures have a size of less than the wavelength of the single photons.

In a preferred embodiment, the first and/or second single photon is detected in one of the diffraction paths of the first and/or second dielectric metastructure grating by a detector, preferably a single photon detector. In a preferred embodiment, the single photon detector is a germanium (Ge), or silicon (Si), or germanium on silicon (Ge on Si) single-photon avalanche diode (SPAD), or Indium gallium arsenide (InGaAs/Inp) single photon detector, or semiconductor-based single-photon avalanche diode (SPAD), or superconducting nanowire single-photon detector (SNSPD), or Silicon Avalanche Photodiodes (Si APD).

In a preferred embodiment, the inventive polarization analysis module is arranged in a quantum cryptography system, preferably a quantum key distribution system, comprising a single photon source and a receiver with one inventive polarization analysis module, whereby the receiver is connected with the single photon source via a quantum channel, and whereby a single photon is generated in the source, transmitted via the quantum channel to the receiver and measured in the at least one inventive polarization analysis module.

In a preferred embodiment, the inventive polarization analysis module is used in a quantum cryptography system for polarization analyses, preferably is used by the receiver.

In a preferred embodiment the single photon source generates single photons in a specific polarization, preferable randomly in one of the two mutually unbiased bases.

In a preferred embodiment, the inventive polarization analysis module is arranged in a quantum cryptography system, preferably a quantum key distribution system, comprising a entangled photon source and at least two receivers with one inventive polarization analysis module each, whereby each receiver is connected with the entangled photon source via a quantum channel, and whereby polarization entangled photon pair with a signal photon and an idler photon is generated in the source, and one photon of each pair is transmitted via the quantum channel to one receiver and measured in the at least one inventive polarization analysis module.

In a preferred embodiment, the receiver comprises a communication module in order to communicate the base of the detection of the single photon with the single photon source or the second receiver. The communication of the base has to be realized in order to generate a key between the single photon source and the one receiver, or between the two receivers.

The above and other aspects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings.

<FIG> shows a first embodiment of the inventive polarization analysis module <NUM>. The polarization analysis module <NUM> comprises a first dielectric metastructure grating <NUM>, a second dielectric metastructure grating <NUM>, a wave-plate <NUM>, and four detectors <NUM>.

As shown in <FIG> the first dielectric metastructure grating <NUM> is arranged in a single photon path <NUM> of first and second single photons. The first dielectric metastructure grating <NUM> transmits or diffracts the first and/or second single photon randomly.

When the first and/or second single photon is diffracted by the first dielectric metastructure grating <NUM> the first and/or second single photon is sent on the +<NUM>st order diffraction path <NUM> or on the -<NUM>st order diffraction path <NUM> to one of the detectors <NUM> where the first and/or second single photon is detected. The first dielectric metastructure grating <NUM> is in the example of <FIG> designed to diffract circular polarized (left L or right R circular polarization) single photons with certainty into the +<NUM>st order diffraction path <NUM> or the -<NUM>st order diffraction path <NUM>. Other polarizations from mutually unbiased bases are diffracted with uncertainty, that means with a probability of <NUM>% in one of the diffraction paths <NUM> or <NUM> of the first dielectric metastructure grating <NUM>. Thus, the first dielectric metastructure grating <NUM> acts as a beam splitting element or as a polarization analysis element for single photons in the L/R base, this means for single photons with left L or right R circular polarization with certainty.

When the first and/or second single photon is transmitted through the first dielectric metastructure grating <NUM>, the first and/or second photon is sent on the <NUM>th order diffraction path <NUM> to the wave-plate <NUM>. The wave-plate <NUM> is in the example of <FIG> a quarter-wave-plate converting the polarization of the first and/or second single photon from circular polarization to linear polarization and vice versa. The second dielectric metastructure grating <NUM> is in the example of <FIG> also designed to diffract circular polarized (left L or right R circular polarization) single photons with certainty into the +<NUM>st order diffraction path <NUM> or the -<NUM>st order diffraction path <NUM>. Together with the quarter-wave-plate <NUM> the second dielectric metastructure grating <NUM> acts as a polarization analysis element for single photons in the H/V base, this means for single photons with horizontal H or vertical V linear polarization with certainty. By a rotation of the quarter-wave-plate <NUM> the base to be measured can be changed to any other base, for example by a rotation of <NUM>° to the +/- base. Due to the wave-plate <NUM> and the second dielectric metastructure grating <NUM> in the example of <FIG> linear polarized single photons are diffracted with certainty into the +<NUM>st order diffraction path <NUM> (for example horizontal linear polarization) or the -<NUM>st order diffraction path <NUM> (for example vertical linear polarization).

As a first non-exclusive example for the inventive polarization analysis module <NUM> and the inventive method in table <NUM> the detection probability of the whole setup from <FIG> is shown for single photons with different polarizations. Output <NUM> means here the probability to detect a single photon in the -<NUM>st order diffraction path <NUM> of the first dielectric metastructure grating <NUM>. Output <NUM> means here the probability to detect a single photon in the +<NUM>st order diffraction path <NUM> of the first dielectric metastructure grating <NUM>. Output <NUM> means here the probability to detect a single photon in the -<NUM>st order diffraction path <NUM> of the second dielectric metastructure grating <NUM>. Output <NUM> means here the probability to detect a single photon in the +<NUM>st order diffraction path <NUM> of the second dielectric metastructure grating <NUM>. In this example the first dielectric metastructure grating <NUM> is a polarization analysis element for single photons in the L/R base when measured in one of the diffraction paths of the first dielectric metastructure grating <NUM>. The wave-plate <NUM> and the second dielectric metastructure grating <NUM> is a polarization analysis element for single photons in the H/V base when measured in one of the diffraction paths of the second dielectric metastructure grating <NUM>.

For a key generation protocol in the example of Table <NUM> the H/V and the R/L bases would be used as mutually unbiased measurement bases. The detection probability shows, that for a single photon with H- or V-Polarization, the first dielectric metastructure grating <NUM> acts as a <NUM>/<NUM> beam splitting element by an overall probability of <NUM>% due to both ±<NUM>st order diffraction in the R/L base and a <NUM>% probability of transmission (shown by the detection in the H/V output). In addition, it can be seen that the first dielectric metastructure grating <NUM> with detection in the output <NUM> and output <NUM> is an analysis in a mutually unbiased base to the H/V base because by the first dielectric metastructure grating <NUM> no information by a detection of a single photon in output <NUM> or output <NUM> can be received because of the same detection probability. When the single photon is detected in the second dielectric metastructure grating <NUM>, meaning here in the H/V base, it can be seen, that the H photon is always detected in the output <NUM>, or a single photon with vertical polarization is always detected in the output <NUM>.

In addition, it can be seen from Table <NUM> that the first dielectric metastructure grating resolves in the R/L bases. In Table <NUM> the input of the + and - polarizations (linear polarization in <NUM> and <NUM> degree) is only shown for the sake of completeness. This base is not used in this example for a key generation protocol.

<FIG> shows the inventive polarizations analysis module <NUM> from <FIG> with an additional polarization rotation element <NUM> in front of the first dielectric metastructure grating <NUM>. By the polarization rotation element <NUM> the base of the analysis for the first dielectric metastructure grating <NUM> can be set for example to an analysis of the +/- bases using a quarter-wave-plate while maintaining the H/V bases of the second dielectric metastructure grating <NUM>.

As a second non-exclusive example for the inventive polarization analysis module <NUM> and the inventive method in table <NUM> the detection probability of the whole setup from <FIG> is shown for different input polarizations. The inputs and outputs in Table <NUM> denote the same as in Table <NUM>. In <FIG> a polariton rotation element, here a quarter-wave-plate at <NUM>° is located in front of the first dielectric metastructure grating <NUM>, leading to a polarization analysis in the two mutually unbiased bases H/V and +/-.

The difference to Table <NUM> is in Table <NUM>, that the polarization analysis takes place in the H/V and the +/- bases and for a key generation protocol these bases would be used.

<FIG> shows the implementation of the inventive polarization analysis module <NUM> in a quantum key distribution (QKD) with a prepare and measure protocol like BB84. A single photon source <NUM> generates single photons one after the other. Each single photon is prepared at a polarization in one of the two orthogonal states of one of the mutually unbiased bases. The single photons are sequentially generated, prepared and sent via a quantum channel <NUM> to the inventive polarization analysis module <NUM>. By the inventive polarization analysis module <NUM> a random base choice out of the two mutually unbiased bases and a polarization analysis is realized. Due to that a key is generated for example with the BB84 protocol.

<FIG> shows the implementation of the inventive polarization analysis module <NUM> in a quantum key distribution (QKD) with an entangled photon source <NUM>. In the example of <FIG> polarization entangled photon pairs, comprising each a signal photon and an idler photon, are generated in the entangled photon source <NUM> one after the other. The signal photon of each pair is sent via a quantum channel <NUM> to a first inventive polarization analysis module <NUM> and the idler photon of each pair is sent via a quantum channel <NUM> to a second inventive polarization analysis module <NUM>. By the inventive polarization analysis module <NUM> a random base choice out of the two mutually unbiased bases and a polarization analysis is realized on the signal and the idler photons. Due to that a key is generated for example with the E91 protocol.

<FIG> shows the inventive polarization analysis module <NUM> from <FIG> used for polarization analysis and the analysis of an additional degree of freedom. The difference to the example of <FIG> is, that in <FIG> the -<NUM>st order diffraction path <NUM> and the +<NUM>st order diffraction path <NUM> are split into several -<NUM>st order diffraction paths <NUM> and +<NUM>st order diffraction paths <NUM> by an additional degree of freedom, for example the wavelength of the single photons. In the example of <FIG> the first dielectric metastructure grating <NUM> acts as a beam splitting element or as a polarization and a second degree of freedom analysis element. The second dielectric metastructure grating <NUM> acts as a polarization and a second degree of freedom analysis element. In dependence of the second degree of freedom, additional detectors are arranged in the multiple ±<NUM>st order diffraction paths.

<FIG> show examples of the first and/or second dielectric metastructure grating <NUM>, <NUM> in top view (<FIG>) and in side view (<FIG>). In this example the multiple cuboid dielectric nano-structures <NUM> consist of a dielectric material with high refractive index (e.g. silicon or titanium dioxide) and the multiple cuboid dielectric nano-structures <NUM> are arranged on a substrate with lower refractive index (e.g. glas). In this example the dielectric metastructure grating consists of a grid of multiple periods of six orientation varying dielectric nano-structures <NUM> each of which dielectric nano-structure <NUM> is rotated by <NUM>° with respect to the previous one, as it can be seen in <FIG>.

Claim 1:
Polarization analysis module (<NUM>), preferably for quantum communication, quantum cryptography, and/or quantum key distribution (QKD), comprises a first and a second diffraction element, a wave-plate (<NUM>), and at least four single photon detectors (<NUM>), in order to enable a polarization analysis of single photons in two mutually unbiased bases and two orthogonal states per base,
wherein the first and second diffraction elements are polarization sensitive first and second dielectric metastructure gratings (<NUM>, <NUM>), and the wave-plate (<NUM>) is arranged between the first and second dielectric metastructure grating (<NUM>, <NUM>), and at least two detectors (<NUM>) are arranged in diffraction paths of the first diffraction element, and at least two detectors (<NUM>) are arranged in diffraction paths of the second diffraction element.