Performance evaluation method and device for non-line-of-sight free space quantum key distribution

Abstract

The invention provides a performance evaluation method and device for non-line-of-sight free space quantum key distribution, and belongs to the technical field of quantum communication and free space optical communication, and the method comprises the steps: constructing a three-dimensional light beam propagation model which comprises light beam drift, light beam broadening and light spot distortion caused by light beam diffraction and atmospheric turbulence; the method comprises the following steps: generating random turbulent flow phase distribution based on a sparse spectrum phase screen method, carrying out numerical simulation on a laser transmission process in combination with a step-by-step propagation algorithm, obtaining a transmissivity sample sequence in which geometric mismatch loss and a turbulent flow fading coupling effect are jointly considered under linear phase shift and secondary phase shift design, and further constructing end-to-end transmissivity probability distribution; and performing weighted evaluation on the key rate of the discrete variable and continuous variable quantum key distribution protocol by using the transmissivity probability distribution to avoid channel fluctuation distortion. The method is suitable for parameters of different turbulence intensities, wavelengths, receiving apertures and channel lengths, and can provide a basis for design and optimization of a non-line-of-sight quantum communication link.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of quantum communication and free space optical communication, and particularly relates to a performance evaluation method and device for non-line-of-sight free space quantum key distribution. BACKGROUND

[0002] The development of quantum computing poses a potential threat to traditional cryptographic systems based on the security assumption of mathematical problems, prompting quantum key distribution technology based on the basic principles of quantum mechanics to become an important secure communication scheme.

[0003] Quantum key distribution systems can be deployed on fiber links or free space optical links. Free space quantum key distribution has the advantages of not needing to lay optical fibers, being suitable for urban environments and complex terrains, etc., but in actual transmission, it is easily affected by atmospheric turbulence, diffraction and obstruction, etc., causing link loss and quantum signal degradation, thereby limiting stability and effective transmission distance. In a non-line-of-sight scenario, due to building or terrain obstruction and deployment restrictions, it is difficult to establish a traditional direct-view free space quantum link. As a structure that can reconfigure the light field, the smart reflector can controllably modulate the phase of the incident light field, actively shape the light beam propagation path, and thus provide a feasible path for constructing a non-line-of-sight quantum communication link.

[0004] However, the propagation path of the smart reflector assisted link is longer and more complex, and the random phase disturbance introduced by turbulence will cause spot drift, broadening and intensity fluctuation, and superimpose with geometric mismatch loss, making the end-to-end transmittance present strong random fluctuations. Transmittance fluctuations will directly affect key performance indicators such as bit error rate and key rate, so a more accurate performance evaluation method is needed. In existing research, some works ignore the influence of turbulence or are only applicable to specific turbulence models, and often consider geometric mismatch loss and turbulence fading as independent factors, which is difficult to reflect the coupling mechanism between diffraction, drift, broadening and distortion; another numerical method based on phase screens and step-by-step propagation does not consider the influence of the smart reflector, resulting in inaccuracy and limitations in estimating the performance of smart reflector assisted non-line-of-sight free space quantum key distribution. SUMMARY

[0005] Therefore, the present application aims to provide a performance evaluation method and device for non-line-of-sight free space quantum key distribution to at least solve one of the problems in the background art.

[0006] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0007] In a first aspect, the present application discloses a performance evaluation method for non-line-of-sight free space quantum key distribution, comprising:

[0008] A three-dimensional beam propagation model is constructed to describe the propagation of the light beam from the transmitting end to the smart reflecting surface and from the smart reflecting surface to the receiving end, and the three-dimensional beam propagation model includes the effects of beam diffraction, beam drift caused by atmospheric turbulence, beam broadening, and spot distortion.

[0009] A phase distribution with random turbulence disturbance is generated based on a sparse spectrum phase screen method, and the phase distribution is embedded into a step-by-step propagation algorithm to numerically simulate the transmission process of laser in an atmospheric channel, to obtain a sample sequence of end-to-end transmittance corresponding to a linear phase shift curve and a quadratic phase shift curve respectively, and reflecting the fluctuation characteristics of the smart reflecting surface assisted channel, and a transmittance probability distribution reflecting the fluctuation characteristics of the smart reflecting surface assisted channel is constructed based on the sample sequence of end-to-end transmittance.

[0010] The transmittance probability distribution is used to evaluate the key rate of discrete variable quantum key distribution protocol and continuous variable quantum key distribution protocol respectively, so as to avoid the distortion of channel fluctuation caused by using average transmittance.

[0011] Further, the end-to-end transmittance is determined by the receiving efficiency, the transmittance caused by atmospheric absorption, and the transmittance considering the coupling effect of geometric mismatch loss and turbulence fading.

[0012] Further, the transmittance considering the coupling effect of geometric mismatch loss and turbulence fading is calculated based on the light intensity distribution within the aperture opening range of the receiving end, which is determined by the receiving end light field amplitude obtained by the step-by-step propagation algorithm.

[0013] Further, the step-by-step propagation algorithm calculates the evolution of the light field within the segmented propagation distance through multi-step iteration, to obtain the receiving end light field amplitude distribution, and the iteration calculation at least includes diffraction evolution based on propagation operator and turbulence phase disturbance superposition based on phase screen.

[0014] Further, the sparse spectrum phase screen method is used to generate a phase screen satisfying the Kolmogorov turbulence statistical characteristics, and the turbulence spectrum is constructed based on the correlation function approximation of atmospheric refractive index fluctuation to form a random phase distribution.

[0015] Further, the initial light field amplitude corresponding to the linear phase shift curve is determined by the beam waist radius and the initial wavefront radius, and the initial light field amplitude corresponding to the quadratic phase shift curve is further determined based on the propagation distance from the smart reflecting surface to the receiving end in addition to the beam waist radius and the initial wavefront radius.

[0016] Further, the weighting evaluation of the key rate comprises: weighting and averaging the function of the key rate with respect to the end-to-end transmittance based on the probability distribution corresponding to the end-to-end transmittance sample sequence to obtain an average key rate.

[0017] Further, the performance evaluation method is applicable to weak turbulence, medium turbulence and strong turbulence conditions.

[0018] Further, the performance evaluation method is applicable to different system parameter configurations, and the system parameters at least include operating wavelength, receiving aperture size and channel length.

[0019] Further, the performance evaluation method is realized by numerical simulation without the need of building a physical experimental system, and is used for the design, parameter configuration and performance optimization of the intelligent reflecting surface assisted non-line-of-sight free space quantum key distribution link.

[0020] In a second aspect, the present application discloses a performance evaluation device for non-line-of-sight free space quantum key distribution, comprising:

[0021] A model construction module is configured to construct a three-dimensional light beam propagation model comprising a transmitting end, an intelligent reflecting surface and a receiving end, and the three-dimensional light beam propagation model comprises light beam diffraction, light beam drift caused by atmospheric turbulence, light beam broadening and light spot distortion effects.

[0022] A phase distribution generation module is configured to generate a phase distribution with random turbulence disturbance based on a sparse spectrum phase screen method.

[0023] A propagation simulation module is configured to combine a step-by-step propagation algorithm to numerically simulate the transmission process of laser in an atmospheric channel to obtain an end-to-end transmittance sample sequence corresponding to a linear phase shift curve and a quadratic phase shift curve respectively.

[0024] A distribution construction module is configured to construct a transmittance probability distribution based on the end-to-end transmittance sample sequence.

[0025] A key rate evaluation module is configured to utilize the transmittance probability distribution to weighting evaluate the key rate of discrete variable quantum key distribution protocols and continuous variable quantum key distribution protocols.

[0026] In a third aspect, the present application discloses a computer readable storage medium having a computer program stored thereon, and the computer program is executed by a processor to realize the performance evaluation method for the intelligent reflecting surface assisted non-line-of-sight free space quantum key distribution.

[0027] Compared with the prior art, the performance evaluation method and device for non-line-of-sight free space quantum key distribution have the following advantages:

[0028] (1) The present application constructs an intelligent reflector assisted three-dimensional light beam propagation model, jointly considers light beam diffraction and light beam drift, light beam broadening and light spot distortion caused by turbulence, so that the light field transmission characteristics of the non-line-of-sight quantum communication link are more complete;

[0029] (2) The present application performs numerical simulation based on the sparse spectrum phase screen method and the step-by-step propagation algorithm, obtains an end-to-end transmittance sample sequence under linear phase shift and quadratic phase shift design, which simultaneously contains the coupling effect of geometric mismatch loss and turbulence fading, and constructs a transmittance probability distribution that can reflect the actual channel fluctuation characteristics;

[0030] (3) The present application uses the transmittance probability distribution to perform weighted evaluation on the key rate of the DV-QKD and CV-QKD protocols, avoids the channel fluctuation distortion caused by only using the average transmittance modeling, and thus improves the evaluation credibility of the system security key indicators;

[0031] (4) The present application has good universality for weak, medium and strong turbulence conditions, and different wavelengths, receiving apertures and channel lengths, and can be evaluated in a pure numerical way without the need to build a physical experimental system, which is convenient for link design, parameter selection and performance optimization. BRIEF DESCRIPTION OF DRAWINGS

[0032] The accompanying drawings, which form a part of the present application, are used to provide a further understanding of the present application, and the illustrative embodiments thereof and their descriptions serve to explain the present application, and do not constitute an improper limitation on the present application. In the drawings:

[0033] Figure 1 The method flowchart described in the embodiments of the present application;

[0034] Figure 2 The key rate of the DV-QKD protocol in the embodiments of the present application under medium to strong turbulence conditions, realized by LPS and QPS curves;

[0035] Figure 3 The key rate of the CV-QKD protocol in the embodiments of the present application under medium to strong turbulence conditions, realized by LPS and QPS curves. DETAILED DESCRIPTION

[0036] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0037] In the description of the present application, it is to be understood by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, which are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features referred to. Therefore, the features defined with "first", "second" and the like can explicitly or implicitly include one or more of the features. In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more.

[0038] In the description of the present application, it should be noted that, unless otherwise specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be connected inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0039] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0040] Professional term explanation:

[0041] IRS: Intelligent Reflective Surface.

[0042] FSO: Free Space Optics.

[0043] QKD: Quantum Key Distribution.

[0044] LPS: Linear Phase Shift.

[0045] QPS: Quadratic Phase Shift.

[0046] DV-QKD: Discrete Variable Quantum Key Distribution.

[0047] CV-QKD: Continuous Variable Quantum Key Distribution.

[0048] SKR: Key Rate.

[0049] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0050] Please refer to Figure 1As shown, the embodiment provides a performance evaluation method for intelligent reflecting surface assisted non-line-of-sight free space quantum key distribution, which specifically includes the following steps:

[0051] Step S101, a three-dimensional beam propagation model under IRS assistance is constructed, which is used to describe the propagation process of the light beam between the transmitting end, the IRS and the receiving end; the three-dimensional propagation model contains the effects of beam diffraction, beam drift caused by atmospheric turbulence, beam widening and spot distortion. Thus, the real transmission behavior of the light beam in the non-line-of-sight quantum communication link is simulated. In the model, the end-to-end free space channel transmittance is represented as:

[0052] ;

[0053] Wherein, represents the IRS assisted free space end-to-end channel transmittance, represents the receiving efficiency, represents the transmittance caused by atmospheric absorption, represents the transmittance considering the coupling effect of geometric loss and turbulence fading.

[0054] Step S102, based on the sparse spectrum phase screen method, a phase distribution with random turbulence disturbance is generated, and the transmission process of laser in the atmospheric channel is numerically simulated by combining the step-by-step propagation algorithm, so as to obtain the transmittance sample sequence under LPS and QPS curves, which contains the coupling effect of geometric mismatch loss and turbulence fading, and the probability distribution of actual IRS assisted end-to-end channel transmittance is constructed.

[0055] In order to construct the light field disturbance in the actual turbulence environment, the sparse spectrum phase screen method is used to generate a random phase distribution with Kolmogorov turbulence characteristics. The turbulence phase screen can be expressed as

[0056] ;

[0057] Wherein, represents the phase screen, represents the fluctuation of atmospheric refractive index, which is expressed by the Markov approximation of the correlation function of the fluctuation:

[0058] ;

[0059] Further, the generated phase screen is embedded in the step-by-step transmission framework, and the receiving end light field amplitude distribution is obtained by iteration, which is expressed as:

[0060] ;

[0061] Wherein, represents the transmission distance at the i th step, ​ Represents the imaginary unit. This represents the change in transmission distance during the m-th transmission step. Indicates wave number, This represents the radial Laplace operator. The amplitude of the optical field transmitted in step 0, i.e., the initial optical field amplitude, is expressed as:

[0062] ;

[0063] in, Indicates the beam waist radius, This represents the initial wavefront radius. For LPS, Regarding QPS, , This indicates the distance from the IRS to the receiver.

[0064] Furthermore, the receiver optical field distribution obtained based on step-by-step propagation The transmittance can be further calculated by considering the coupling effect of geometric mismatch loss and turbulent fading. Its formula is expressed as:

[0065] ;

[0066] in, Indicates the aperture opening at the receiving end. Indicates light intensity. Indicates the amplitude of the light field. This represents a vector on a plane perpendicular to the path of the light beam. Indicates the transmission distance.

[0067] S103. Use the obtained transmittance distribution to perform a weighted evaluation of the key rates of DV-QKD and CV-QKD, avoiding channel fluctuation distortion caused by using average transmittance modeling.

[0068] Based on the transmittance distribution obtained from simulation, a weighted average of the key rates is applied to avoid channel fluctuation distortion caused by using average transmittance modeling. The formula for calculating the weighted average of the key rates is as follows:

[0069] ;

[0070] in, Indicates the pulse duration. Indicates end-to-end channel transmittance The probability distribution, This indicates that the key rate of QKD is related to The function is... Key rate analysis for DV-QKD and CV-QKD under Gaussian modulation is relatively mature in the field, so it is not elaborated here.

[0071] When the simulation experiment is performed based on the above method, Table 1 is the parameter value of the free space communication system, and Tables 2 and 3 are the simulation parameters of DV-QKD and CV-QKD respectively.

[0072] Table 1 is as follows:

[0073]

[0074] Table 2 is as follows:

[0075]

[0076] Table 3 is as follows:

[0077]

[0078] Figure 2 Based on the simulation parameters shown in Tables 1 and 2, the achievable key rate of DV-QKD is given, and the solid line and the dashed line represent the simulation results of QPS and LPS curves respectively. It can be seen from the figure that the method can evaluate the performance of IRS-aided FSO DV-QKD, and clearly shows the advantage of QPS compared with LPS in improving the average key rate.

[0079] Figure 3 Based on the simulation parameters shown in Tables 1 and 3, the achievable key rate of CV-QKD is shown, and the solid line and the dashed line represent the simulation results of QPS and LPS curves respectively. It can be seen from the figure that the method is also applicable to CV-QKD, and the numerical simulation result correctly reflects the characteristic that QPS can effectively improve the average key rate compared with LPS.

[0080] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the specification of the present application.

[0081] The above is only the preferred embodiment of the present application, and is not used to limit the present application, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A performance evaluation method for non-line-of-sight free-space quantum key distribution, characterized in that, include: A three-dimensional beam propagation model is constructed, which includes a transmitter, a smart reflector, and a receiver, to describe the propagation process of the beam from the transmitter to the smart reflector and from the smart reflector to the receiver. The three-dimensional beam propagation model also includes beam diffraction, beam drift caused by atmospheric turbulence, beam broadening, and beam distortion effects. A phase distribution with random turbulent disturbances is generated based on the sparse spectrum phase screen method, and the phase distribution is embedded into the step propagation algorithm to numerically simulate the transmission process of laser in the atmospheric channel. This yields an end-to-end transmittance sample sequence that corresponds to linear phase shift curves and quadratic phase shift curves, and simultaneously includes the coupling effect of geometric mismatch loss and turbulent fading. In this way, an end-to-end transmittance probability distribution is constructed. The key rates of discrete-variable quantum key distribution protocols and continuous-variable quantum key distribution protocols are evaluated using the transmittance probability distribution to avoid channel fluctuation distortion caused by modeling with average transmittance.

2. The performance evaluation method for non-line-of-sight free-space quantum key distribution according to claim 1, characterized in that, The end-to-end transmittance is determined by the receiving efficiency, the transmittance caused by atmospheric absorption, and the transmittance that takes into account the coupling effect of geometric mismatch loss and turbulent fading.

3. The performance evaluation method for non-line-of-sight free-space quantum key distribution according to claim 2, characterized in that, The transmittance, which takes into account the coupling effect of geometric mismatch loss and turbulent fading, is calculated based on the light intensity distribution within the aperture range of the receiver. The light intensity distribution is determined by the receiver light field amplitude obtained by the step-by-step propagation algorithm.

4. The performance evaluation method for non-line-of-sight free-space quantum key distribution according to claim 1, characterized in that, The step-by-step propagation algorithm calculates the evolution of the light field within the segmented propagation distance through multi-step iterative calculations to obtain the amplitude distribution of the light field at the receiving end. The iterative calculation includes at least diffraction evolution based on the propagation operator and superposition of turbulent phase disturbances based on the phase screen.

5. The performance evaluation method for non-line-of-sight free-space quantum key distribution according to claim 1, characterized in that, The sparse spectrum phase screen method is used to generate a phase screen that satisfies the statistical characteristics of Kolmogorov turbulence, and the turbulence spectrum is approximately constructed based on the correlation function of atmospheric refractive index fluctuations to form a random phase distribution.

6. The performance evaluation method for non-line-of-sight free-space quantum key distribution according to claim 1, characterized in that, The initial optical field amplitude corresponding to the linear phase shift curve is determined by the beam waist radius and the initial wavefront radius. The initial optical field amplitude corresponding to the quadratic phase shift curve is further determined by combining the beam waist radius and the initial wavefront radius with the propagation distance from the smart reflector to the receiver.

7. The performance evaluation method for non-line-of-sight free-space quantum key distribution according to claim 1, characterized in that, The weighted evaluation of the key rate for the discrete-variable quantum key distribution protocol and the continuous-variable quantum key distribution protocol includes: based on the probability distribution corresponding to the end-to-end transmittance sample sequence, performing a weighted average of the key rate as a function of the end-to-end transmittance to obtain the average key rate.

8. A performance evaluation device for non-line-of-sight free-space quantum key distribution, characterized in that, include: The model building module is used to build a three-dimensional beam propagation model that includes a transmitter, a smart reflector and a receiver. The three-dimensional beam propagation model also includes beam diffraction, beam drift caused by atmospheric turbulence, beam broadening and spot distortion effects. The phase distribution generation module is used to generate a phase distribution with random turbulent perturbations based on the sparse spectral phase screen method. The propagation simulation module is used to numerically simulate the transmission process of laser in atmospheric channels by combining the step-by-step propagation algorithm, and obtain end-to-end transmittance sample sequences corresponding to linear phase shift curves and quadratic phase shift curves, respectively. A distribution construction module is used to construct a transmittance probability distribution based on the end-to-end transmittance sample sequence; The key rate evaluation module is used to perform a weighted evaluation of the key rates of discrete variable quantum key distribution protocols and continuous variable quantum key distribution protocols using the transmittance probability distribution.

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