Method for analyzing influence of optical amplifier on quantum key distribution performance in satellite-ground link

Abstract

The invention relates to a method for analyzing the influence of an optical amplifier on quantum key distribution performance in a satellite-ground link, and the method comprises the steps: constructing a satellite-ground link quantum channel model; according to the satellite-ground link quantum channel model, obtaining total signal loss; the communication sender and the communication receiver calculate the security key rate of the system under the condition of collective attack through a first formula by adopting a reverse coordination mode; an optical amplifier is inserted between the output end of a free space channel and the input end of a communication receiver detection device, the effect of the optical amplifier on signals is described by using a corresponding transformation matrix according to the characteristics of the optical amplifier, a modulation protocol is simulated to obtain the corrected noise amount of homodyne detection and heterodyne detection, and the corrected noise amount of the homodyne detection and the heterodyne detection is calculated. And calculating the corrected security key rate. According to the method, the influence of the optical amplifier on the key distribution performance closer to reality can be obtained, stable and efficient key distribution is guaranteed, the communication safety and efficiency are guaranteed, and the optimal configuration of the performance of the quantum key distribution system is achieved.

Description

Background Art

[0002] In the field of quantum communication, quantum key distribution (QKD) has attracted much attention as a key technology to ensure communication security. QKD enables both parties to share a key with information-theoretic security in the presence of interference from eavesdroppers. Free-space quantum key distribution has become a research hotspot for achieving long-distance and even global quantum communication due to its significant flexibility in infrastructure construction and mobility, especially in the field of satellite communications, where its application prospects are broad.

[0003] Continuous variable quantum key distribution (CV-QKD) has become a promising research direction in this field because it is highly compatible with optical fiber communication systems and is economical. Discrete modulation continuous variable quantum key distribution (DM-CV-QKD) can apply efficient low-density parity-check codes (LDPC) in the post-processing process of extracting keys, which effectively improves the reliability and error correction capability of the keys, and also shows higher coordination efficiency under low signal-to-noise ratio conditions.

[0004] In the prior art, there are methods for improving the key rate of quaternary discrete modulation quantum key distribution protocols by adding a preamplifier at the output end of the quantum channel of the optical fiber system, and methods for improving the key generation rate of quaternary and octal discrete modulation continuous variable quantum key distribution protocols in short-distance communications by introducing optical amplifiers in satellite-to-ground links. However, in the satellite-to-ground link scenario, the degradation area is large, which makes it difficult for the safe communication distance to meet actual needs, so that the key rate drops rapidly during long-distance satellite-to-ground link communications, and stable and efficient key distribution cannot be guaranteed, which seriously affects the security and efficiency of communications; and in the complex satellite-to-ground link environment, the optical signal transmission of the optical amplifier will be affected by environmental factors such as turbulence intensity, optical wavelength and horizontal elevation angle, which in turn affects the performance of the optical amplifier, resulting in a sharp drop in the key rate or even failure to communicate normally; finally, the optical amplifier has different synergies with different modulation modes, which makes it impossible to fully realize the potential of the optical amplifier under different modulation modes, and it is difficult to achieve the optimal configuration of the performance of the quantum key distribution system.

[0005] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0006] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0007] The purpose of the embodiments of the present disclosure is to provide a method for analyzing the impact of optical amplifiers in satellite-to-ground links on quantum key distribution performance, thereby overcoming one or more problems caused by limitations and defects of related technologies at least to a certain extent.

[0008] The present application provides a method for analyzing the impact of an optical amplifier on quantum key distribution performance in a satellite-to-ground link, including:

[0009] A quantum channel model for the satellite-to-ground link is constructed based on the atmospheric thickness, the vertical distance from the near-Earth satellite to the ground, the horizontal elevation angle of the ground observation station, the total distance from the near-Earth satellite to the ground observation station, and the effective distance from the observation station to the outer atmosphere.

[0010] According to the satellite-to-ground link quantum channel model, a total signal loss is obtained; the total signal loss includes: geometric loss, scattering loss per kilometer and scintillation loss, wherein the geometric loss is obtained according to the vertical distance from the near-earth satellite to the ground, and the scattering loss per kilometer and the scintillation loss are obtained according to the effective atmospheric thickness and atmospheric visibility;

[0011] The communication sender and the communication receiver use a reverse coordination method to calculate the security key rate of the system under collective attack by a first formula; the first formula is SKR = βI(A; B) - χ Holevo (B; E), where β is the reverse regulation efficiency, I(A; B) is the mutual information between the communication sender and the communication receiver, and χ Holevo (B; E) is the upper limit of the mutual information between the communication interference party and the communication receiving party; the mutual information between the communication sending party and the communication receiving party is calculated by the noise amount associated with the modulation variance and the homodyne detection or heterodyne detection;

[0012] An optical amplifier is inserted between the output end of the free space channel and the input end of the communication receiving party detection device. According to the characteristics of the optical amplifier, the corresponding transformation matrix is ​​used to describe the effect of the optical amplifier on the signal. The modulation protocol is simulated to obtain the corrected noise amount of homodyne detection and heterodyne detection, and the corrected security key rate is calculated.

[0013] In a possible implementation, the total distance from the near-Earth satellite to the ground observation station is calculated using a second formula;

[0014] The second formula is:

[0015] Among them, L tot is the total distance from the near-Earth satellite to the ground observation station, R is the radius of the Earth, L saz is the vertical distance from the near-Earth satellite to the ground,

[0016] In a possible implementation, the effective distance between the observation station and the outer periphery of the atmosphere is calculated by a third formula;

[0017] The third formula is:

[0018]

[0019] Among them, L atmeff is the effective atmospheric thickness, L atm is the thickness of the atmosphere,

[0020] is the horizontal elevation angle of the ground observation station.

[0021] In a possible implementation manner, the total signal loss formula is:

[0022] α tot =α geo +α scat ·L atmeff +α sci ;

[0023] Among them, α tot is the total signal loss, α geo is the geometric loss, α scat is the scattering loss per kilometer, α sci Flicker loss.

[0024] In a possible implementation, the geometric loss formula is:

[0025]

[0026] Where λ is the signal wavelength, D t is the aperture diameter of the transmitting telescope, D r is the aperture diameter of the receiving telescope, T t is the transmittance of the transmitting telescope, T r is the transmittance of the receiving telescope, L p is the pointing loss efficiency, L rot ≥D t D t / λ.

[0027] In a possible implementation manner, the scattering loss formula per kilometer is:

[0028]

[0029] Among them, V is the atmospheric visibility, and p is the scattering index;

[0030]

[0031] In a possible implementation manner, the flicker loss formula is:

[0032]

[0033] Among them, p thris the probability threshold, is the intensity flicker index;

[0034]

[0035] in, is the refractive index structure constant.

[0036] In a possible implementation manner, the mutual information amount between the communication sender and the communication receiver is calculated by the fourth formula, and the upper limit of the mutual information amount between the communication interferer and the communication receiver is calculated by the fifth formula;

[0037] The fourth formula is:

[0038] Wherein, d is the detection mode parameter. When d=1, it is homodyne detection. When d=2, it is heterodyne detection. V=V A +1, V A is the modulation variance, χ tot is the total noise, ε is the channel excess noise, χ line is the total added noise of the channel in units of shot noise, χ hom / het is the amount of noise associated with homodyne or heterodyne detection, and T is the channel transmittance;

[0039] The fifth formula is: Holevo (B; E) = S(ρ E )-∑ v p(y)S(ρ E / y );

[0040] Where S is the von Neumann entropy of the quantum state held by the communication interferer.

[0041] In a possible implementation manner, the steps of inserting an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device, using a corresponding transformation matrix to describe the effect of the optical amplifier on the signal according to the characteristics of the optical amplifier, simulating the parameters of the modulation protocol, obtaining the corrected noise amount of homodyne detection and heterodyne detection, and calculating the corrected security key rate include:

[0042] Insert an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device; wherein the optical amplifier includes: a phase-sensitive amplifier and a phase-insensitive amplifier;

[0043] When the optical amplifier is a phase-sensitive amplifier, the behavior of the phase-sensitive amplifier is described by a first transformation matrix, and when the optical amplifier is a phase-insensitive amplifier, the behavior of the phase-insensitive amplifier is described by a second transformation matrix; wherein the first transformation matrix is The second transformation matrix is g is the gain multiple of the optical amplifier;

[0044] The M-DM-CVQKD modulation protocol, the d16-DM-CVQKD modulation protocol, and the Gaussian modulation protocol are simulated to obtain the noise amount of homodyne detection and heterodyne detection, and the Gaussian protocol correction noise amount is applied to the M-DM-CVQKD modulation protocol and the d16-DM-CVQKD modulation protocol to obtain the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount; wherein the corrected homodyne detection noise amount is calculated by the sixth formula, and the corrected heterodyne detection noise amount is calculated by the seventh formula; the sixth formula is The seventh formula is η is the detection efficiency of the detector, v el is the electrical noise, N is the inherent noise of the non-degenerate optical parametric amplifier;

[0045] Substituting the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount into the first formula, a corrected security key rate is obtained.

[0046] In a possible implementation manner, after inserting an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device, using a corresponding transformation matrix to describe the effect of the optical amplifier on the signal according to the characteristics of the optical amplifier, simulating the modulation protocol to obtain the corrected noise amount of homodyne detection and heterodyne detection, and calculating the corrected security key rate, the method further includes:

[0047] The gain in security key rate after adding the optical amplifier is measured by the improvement ratio, and the calculation formula of the improvement ratio is: Among them, K R is the security key rate, and L is the communication distance.

[0048] The technical solution provided by this application may have the following beneficial effects:

[0049] Through the analysis method of the influence of optical amplifiers on quantum key distribution performance in the satellite-to-ground link of the present application, it is possible to construct a satellite-to-ground link quantum channel model, deeply analyze the signal loss mechanism, accurately calculate the key rate, and introduce a new hexadecimal dual-ring modulation method to correct the progressive key rate after adding the optical amplifier, thereby obtaining a more practical influence of the optical amplifier on the key distribution performance, thereby ensuring the actual needs of the safe communication distance, ensuring stable and efficient key distribution, ensuring communication security and efficiency, and achieving the optimal configuration of the quantum key distribution system performance.

[0050] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0052] Figure 1 A flow chart showing a method for analyzing the impact of an optical amplifier in a satellite-to-ground link on quantum key distribution performance in an exemplary embodiment of the present disclosure;

[0053] Figure 2 A schematic diagram of a satellite-to-ground channel model showing a method for analyzing the impact of an optical amplifier in a satellite-to-ground link on quantum key distribution performance in an exemplary embodiment of the present disclosure;

[0054] Figure 3 A schematic diagram showing the relationship between the geometric loss of different wavelengths and the distance from the satellite to the ground observation station in an exemplary embodiment of the present disclosure;

[0055] Figure 4 A schematic diagram showing the relationship between the Renov variance at different wavelengths and the effective atmospheric thickness in an exemplary embodiment of the present disclosure;

[0056] Figure 5 A schematic diagram showing the relationship between scintillation loss and effective atmospheric thickness at different wavelengths and receiving apertures in an exemplary embodiment of the present disclosure;

[0057] Figure 6 The constellation diagrams of 8-DM-CVQKD, 16-DM-CVQKD, and d16-DM-CVQKD protocols in the optical phase space in the exemplary embodiments of the present disclosure are shown;

[0058] Figure 7A detailed flow chart showing step S400 of a method for analyzing the impact of an optical amplifier in a satellite-to-ground link on quantum key distribution performance in an exemplary embodiment of the present disclosure;

[0059] Figure 8 Z and modulation variance V showing the analysis method of the influence of optical amplifiers in satellite-to-ground links on quantum key distribution performance in an exemplary embodiment of the present disclosure A Relationship diagram;

[0060] Fig. 9 A graph showing the relationship between the security key rate and the distance under heterodyne detection of the 8-DM-CVQKD system in an exemplary embodiment of the present disclosure at different amplification gains;

[0061] Fig.10 A graph showing the relationship between the security key rate and the distance under different amplification gains in the d16-DM-CVQKD heterodyne detection in an exemplary embodiment of the present disclosure is shown;

[0062] Fig.11 A graph showing the relationship between the 8-DM-CVQKD improvement ratio G and the distance in an exemplary embodiment of the present disclosure is shown;

[0063] Fig.12 The influence of channel excess noise on the distance and improvement ratio G in the 8-DM-CVQKD system in the exemplary embodiment of the present disclosure is shown;

[0064] Fig.13 A graph showing the relationship between the d16-DM-CVQKD improvement ratio G and the communication distance in an exemplary embodiment of the present disclosure is shown;

[0065] Fig.14 A graph showing the relationship between the d16-DM-CVQKD improvement ratio G and the communication distance in different channel noise in an exemplary embodiment of the present disclosure is shown;

[0066] Fig.15 The relationship between the progressive key rate and the distance from the satellite to the ground, the weak turbulence intensity, and the horizontal elevation angle in the exemplary embodiment of the present disclosure is shown.

[0067] Fig.16 The relationship between the progressive key rate and the distance from the satellite to the ground, the weak turbulence intensity, and the horizontal elevation angle in the exemplary embodiment of the present disclosure is shown.

[0068] Fig.17 The relationship between the progressive key rate and the distance from the satellite to the ground, the intensity of strong turbulence, and the horizontal elevation angle in the exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0069] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0070] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0071] In this example implementation, a method for analyzing the impact of an optical amplifier in a satellite-to-ground link on quantum key distribution performance is first provided. The method can be applied to a terminal device, such as a mobile phone, a desktop computer, a personal digital assistant, a laptop computer, a tablet computer, a smart watch, or other mobile terminal. Figure 1 As shown in , the method may include the following steps:

[0072] Step S100: constructing a satellite-to-ground link quantum channel model according to the atmospheric thickness, the vertical distance from the near-Earth satellite to the ground, the horizontal elevation angle of the ground observation station, the total distance from the near-Earth satellite to the ground observation station and the effective distance between the observation station and the outer periphery of the atmosphere.

[0073] Step S200: According to the satellite-to-ground link quantum channel model, a total signal loss is obtained; the total signal loss includes: geometric loss, scattering loss per kilometer and scintillation loss, wherein the geometric loss is obtained according to the vertical distance from the near-earth satellite to the ground, and the scattering loss per kilometer and the scintillation loss are obtained according to the effective atmospheric thickness and the atmospheric visibility.

[0074] Step S300: The communication sender (i.e. Alice) and the communication receiver (i.e. Bob) use a reverse coordination method to calculate the security key rate of the system under collective attack by using the first formula; the first formula is SKR = βI(A; B) - χ Holevo (B; E), where β is the reverse regulation efficiency, I(A; B) is the mutual information between the communication sender and the communication receiver, and χ Holevo(B; E) is the upper limit of the mutual information between the communication interference party (ie, Eve) and the communication receiving party; the mutual information between the communication sender and the communication receiving party is calculated by the amount of noise associated with the modulation variance and homodyne detection or heterodyne detection.

[0075] Step S400: insert an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device, use the corresponding transformation matrix to describe the effect of the optical amplifier on the signal according to the characteristics of the optical amplifier, simulate the modulation protocol to obtain the corrected noise amount of homodyne detection and heterodyne detection, and calculate the corrected security key rate.

[0076] The above method can deeply analyze the signal loss mechanism by constructing a quantum channel model of the satellite-to-ground link, and calculate the security key rate of the system under collective attack through reverse coordination. At the same time, an optical amplifier is added, and according to the characteristics of the optical amplifier, the modulation protocol is simulated to obtain the corrected noise amount of homodyne detection and heterodyne detection, and the security key rate is corrected to obtain an accurate security key rate. Therefore, after adding the optical amplifier, the actual requirements of the secure communication distance are ensured, stable and efficient key distribution is guaranteed, communication security and efficiency are guaranteed, and the optimal configuration of the performance of the quantum key distribution system is achieved.

[0077] Next, we will refer to Figures 1 to 7 Each step of the above method in this example implementation is described in more detail.

[0078] In step S100, a satellite-to-ground link quantum channel model is constructed according to the atmospheric thickness, the vertical distance from the low-Earth satellite to the ground, the horizontal elevation angle of the ground observation station, the total distance from the low-Earth satellite to the ground observation station, and the effective distance between the observation station and the outer periphery of the atmosphere.

[0079] It should be noted that, by determining the key geometric parameters and variable relationships of the satellite-to-ground link quantum channel in step S100, the basic framework of the entire research is constructed, providing a unified model and parameter basis for the subsequent analysis of the transmission characteristics of the signal in the link and the calculation of the key rate.

[0080] In one embodiment, Figure 2 As shown, the total distance from the near-Earth satellite to the ground observation station is calculated by the second formula, and the effective distance from the observation station to the outer periphery of the atmosphere is calculated by the third formula;

[0081] The second formula is:

[0082]

[0083] The third formula is:

[0084]

[0085] Among them, L tot is the total distance from the low-earth orbit satellite to the ground observation station, R is the radius of the earth, and L saz is the vertical distance from the low-earth orbit satellite to the ground, and L atmeff is the effective atmospheric thickness, and L atm is the atmospheric thickness,

[0086] is the horizontal elevation angle of the ground observation station.

[0088] It can be understood that the effective atmospheric thickness is the effective distance between the observation station and the outer periphery of the atmosphere.

[0089] In step S200, according to the satellite-ground link quantum channel model, the total signal loss is obtained; the total signal loss includes: geometric loss, scattering loss per kilometer, and scintillation loss. Among them, the geometric loss is obtained according to the vertical distance from the low-earth orbit satellite to the ground, and the scattering loss per kilometer and the scintillation loss are obtained according to the effective atmospheric thickness and the atmospheric visibility.

[0090] It can be understood that in the satellite-ground link, the communication channel is free space. Different from the high stability of the optical fiber channel, this channel is more likely to cause signal loss between the satellite and the ground station; the main losses include: geometric loss caused by the satellite position, scattering loss per kilometer caused by atmospheric aerosol, and scintillation loss caused by atmospheric turbulence.

[0091] In one embodiment, the total signal loss formula is:

[0092] α tot = α geo + α scat ·L atmeff + α sci ;

[0093] Among them, α tot is the total signal loss, α geo is the geometric loss, α scat is the scattering loss per kilometer, and α sci is the scintillation loss. Under the same horizontal elevation angle, the geometric loss depends on the vertical distance from the satellite to the ground, and the degrees of the scattering loss per kilometer and the scintillation loss depend on the atmospheric visibility and the effective atmospheric thickness.

[0094] The geometric loss formula is:

[0095] Among them, α geo is the geometric loss, λ is the signal wavelength, D t is the diameter of the transmitting telescope aperture, D r is the diameter of the receiving telescope aperture, Tt is the transmittance of the transmitting telescope, T r is the transmittance of the receiving telescope, L p is the pointing loss efficiency, L tot ≥D r D t / λ.

[0096] It can be understood that the geometric loss is defined as the ratio of the average transmitted power to the received power measured at the entrance and exit of the transmitting telescope and the receiving telescope, that is, the communication sender and the communication receiver are in the far field. Figure 3 As shown in the figure, the geometric loss increases with the total distance from the near-Earth satellite to the ground observation station, and the wavelength of the transmitted light is also an important factor affecting the geometric loss. The overall change trends of the three wavelengths are consistent, and the larger the wavelength, the greater the geometric loss.

[0097] The formula for the scattering loss per kilometer is:

[0098] Among them, α scat is the scattering loss per kilometer, V is the atmospheric visibility, and p is the scattering index;

[0099]

[0100] It is understandable that the scattering loss of the Kruse and Kim model depends on the wavelength of the signal and the atmospheric visibility. According to the formula for scattering loss per kilometer, the loss per kilometer is multiplied by the effective atmospheric thickness. There is an inverse relationship between the scattering loss per kilometer and the wavelength, and the p value takes different values ​​depending on the visibility. Generally speaking, in good weather conditions, the atmospheric visibility V = 200 km, and in conditions with dust, haze, etc., the atmospheric visibility V = 20 km.

[0101] The flicker loss formula is:

[0102] Among them, p thr is the probability threshold, is the intensity flicker index;

[0103]

[0104] in, for is the refractive index structure constant.

[0105] It is understandable that if Figure 4 As shown, and The same is the effective atmospheric thickness L atmeff Function of intensity flicker index Using Rytov variance to estimate; usually visibility is good, that is, at a weak turbulence level Take 10 -16 . use The expression simulates the relationship between the Rytov variance and the effective atmospheric thickness at wavelengths of 850nm, 1550nm, and 3800nm ​​under weak turbulence levels. Under weak turbulence levels, the effective atmospheric distance is between 20km and 40km. The value does not exceed 3.5.

[0106] When the flicker loss is within 1.1dB error, and 0.7>p thr >2×10 -7 You can The relationship between the simulated scintillation loss and the effective atmospheric thickness at wavelengths of 850nm, 1550nm, 3800nm ​​and different receiving apertures is shown in Figure 2. Figure 5 As shown, the receiving aperture and wavelength have an impact on the flicker loss. The receiving aperture parameters can affect the changing trend of the flicker loss. Increasing the aperture diameter of the receiver can reduce the flicker loss during the communication process. Under the same receiving aperture, the larger the wavelength, the greater the flicker loss, and the changing trend of the flicker loss affected by different wavelengths is consistent.

[0107] In one embodiment, the mutual information between the communication sender and the communication receiver is calculated by the fourth formula, and the upper limit of the mutual information between the communication interferer and the communication receiver is calculated by the fifth formula;

[0108] The fourth formula is:

[0109] Wherein, d is the detection mode parameter. When d=1, it is homodyne detection. When d=2, it is heterodyne detection. V=V A +1, V A is the modulation variance, χ tot is the total noise, ε is the channel excess noise, χ line is the total added noise of the channel in units of shot noise, χ hom / het is the amount of noise associated with homodyne or heterodyne detection, and T is the channel transmittance.

[0110] The fifth formula is: Holevo (B; E) = S(ρ E )-∑ v p(y)S(ρ E / y ).

[0111] Where S is the von Neumann entropy of the quantum state held by the communication interferer.

[0112] It can be understood that the fifth formula can be obtained by the covariance matrix γ of the bipartite state AB The symplectic eigenvalues ​​of γ are calculated. AB It is transmitted through a quantum channel with channel transmittance T and channel excess noise ε, and projection measurement is performed after reaching the communication receiving end. The covariance matrix is ​​as follows:

[0113]

[0114] λ i (i=1,2,3,4) is the covariance matrix γ AB The symplectic eigenvalues ​​of .

[0115]

[0116] Where G(x) = (1+x)log 2 (1+x)-xlog 2 (x), I 2 =diag(1,1),σ Z =diag(1,-1), Z N is the correlation coefficient between the in-phase component and the orthogonal component of discrete modulation, in, The density matrix τ is used to describe the state of the communication sender. and represent the annihilation and generation operators respectively, ε and T are the channel over-noise and channel transmittance. After the quantum transmission phase is over, the classical post-processing phase begins immediately. The communication sender and the communication receiver conduct reverse reconciliation and finally obtain a string of security keys.

[0117] It should be noted that the phase diagrams of M-DM-CVQKD and d16-DM-CVQKD modulation are shown in Figure 6 As shown, d16-DM-CVQKD is a hexadecimal dual-ring discrete modulation quantum key distribution. The communication sender selects M = 2 L (L=1,2,...) base modulation, assuming that each state is selected The probability of is equal, R is the number of rings, is the average number of photons, and the modulation variance V A The relationship with the average photon number is V A =2a 2 , for the d16-DM-CVQKD modulation with two loops, the inner loop Outer Ring Adjust the ratio of inner and outer rings Maximize the key rate.

[0118] In step S400, an optical amplifier is inserted between the output end of the free space channel and the input end of the communication receiving party detection device. According to the characteristics of the optical amplifier, the corresponding transformation matrix is ​​used to describe the effect of the optical amplifier on the signal, the modulation protocol is simulated to obtain the corrected noise amount of homodyne detection and heterodyne detection, and the corrected security key rate is calculated.

[0119] It is understandable that optical amplifiers are key devices for enhancing the strength and quality of optical signals and are widely used in optical communication systems, especially in long-distance signal transmission.

[0120] In one embodiment, Figure 7 As shown, step S400 may include the following sub-steps:

[0121] In step S410, an optical amplifier is inserted between the output end of the free space channel and the input end of the communication receiving party detection device; wherein the optical amplifier includes: a phase sensitive amplifier and a phase insensitive amplifier.

[0122] It can be understood that two typical optical amplifiers are inserted between the output end of the free space channel and the input end of the communication receiving party detection device: a phase sensitive amplifier (PSA) and a phase insensitive amplifier (PIA), wherein the attenuation coefficient α of the signal is set to 0.2dB / km, and the channel excess noise is set to ε=0.001.

[0123] In step S420, when the optical amplifier is a phase-sensitive amplifier, the behavior of the phase-sensitive amplifier is described by a first transformation matrix, and when the optical amplifier is a phase-insensitive amplifier, the behavior of the phase-insensitive amplifier is described by a second transformation matrix; wherein the first transformation matrix is The second transformation matrix is g is the gain multiple of the optical amplifier.

[0124] It can be understood that the PSA is a degenerate optical parametric amplifier that ideally allows noiseless amplification for a selected orthogonal value, g ≥ 1; the PIA is a non-degenerate optical parametric amplifier that symmetrically amplifies two orthogonal components, and its amplification process is associated with a fundamental excess noise that is generated by the coupling of the signal input to the internal mode of the amplifier. This type of amplifier can be modeled as a noiseless amplifier by applying an appropriate gain factor to each input mode and using EPR states of variance N, half of which enter the second input port of the amplifier to simulate the intrinsic noise of the amplifier.

[0125] In step S430, simulate the M-DM-CVQKD modulation protocol, the d16-DM-CVQKD modulation protocol, and the Gaussian modulation protocol to obtain the noise amounts of homodyne detection and heterodyne detection, and apply the corrected noise amount of the Gaussian protocol to the M-DM-CVQKD modulation protocol and the d16-DM-CVQKD modulation protocol to obtain the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount; where, the corrected homodyne detection noise amount is calculated by the sixth formula, and the corrected heterodyne detection noise amount is calculated by the seventh formula; the sixth formula is The seventh formula is η is the detection efficiency of the detector, v el is the electrical noise, and N is the inherent noise of the non-degenerate optical parametric amplifier.

[0126] It can be understood that for discrete modulation continuous variable quantum key distribution, it is a prerequisite for the communication sender to reasonably select the modulation variance V A to complete the key distribution. Through Gaussian modulation simulate the relationship between Z and the modulation variance in the Gaussian protocol, the 4-DM-CVQKD protocol, the 8-DM-CVQKD protocol, the 16-DM-CVQKD protocol, and the d16-DM-CVQKD protocol, as Figure 8 shown. It can be seen that when the modulation variance is very small, the M-DM-CVQKD and d16-DM-CVQKD modulations are very close to the CVQKD protocol based on Gaussian modulation. Therefore, the noise results of the CVQKD protocol detector under homodyne detection and heterodyne detection can be used in the M-DM-CVQKD and d16-DM-CVQKD modulation protocols to obtain the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount.

[0127] In step S440, substitute the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount into the first formula to obtain the corrected secure key rate.

[0128] It can be understood that according to the first formula and the fourth formula, substituting χ hom / het in the fourth formula with or thus obtaining the corrected secure key rate. For example, when exploring the security performance analysis of adding a PIA amplifier to the system under heterodyne detection, substitute χ hom / het in the fourth formula with

[0129] Furthermore, after step S400, it further includes:

[0130] Step S500, the gain of the security key rate after adding the optical amplifier is measured by the improvement ratio, and the calculation formula of the improvement ratio is: Among them, K R is the security key rate, and L is the communication distance.

[0131] In one embodiment, the performance of quantum key distribution of optical amplifiers in satellite-to-ground links is analyzed by the technical solution of the present application:

[0132] Transmitting telescope aperture diameter D t , receiving telescope aperture diameter D r , transmittance of the transmitting telescope T t , receiving telescope transmittance T r , pointing loss efficiency L p , Renouf variance Probability threshold p thr The simulation parameters of the reverse regulation efficiency β are shown in the following table:

[0133]

[0134] like Figure 9-10 As shown in the figure, the relationship between the security key rate and distance under heterodyne detection for the 8-DM-CVQKD and d16-DM-CVQKD systems is shown, where the modulation variance has been adjusted to the optimal value. It can be understood that in practical applications, only when the key rate is greater than 0 can the communication sender and the communication receiver extract the unknown key from the information exchanged between them. However, since the key rate is too small and has no practical significance, only the key rate SKR ≥ 10 is considered here. -7 It can be seen that the gain g of the optical amplifier can effectively improve the generation of the key rate within a certain range. When g = 1, it means that the system has not added an optical amplifier, and the quantum key rate at this time is used as the benchmark. It can be seen from the figure that although the curve changes little under different gain values, the addition of the optical amplifier can still bring about an improvement in the key rate.

[0135] When the improvement ratio G is introduced to measure the effect of the gain, such as Fig.11 As shown, the point P(Px, Py) corresponds to Fig. 9The intersection of g=1 and g=20 in the figure, the two have the same meaning. It can be observed from the figure that the amplification effect of the optical amplifier on the key rate is not effective at all secure transmission distances. Specifically, within the transmission distance range from 0 to Px, the amplifier can still play an amplifying role and improve the signal quality. This part is called the "enhancement region". However, when the transmission distance exceeds Px, the improvement ratio begins to become negative, and the curve drops rapidly, entering the "degradation region". At this time, the proportion of the degradation region can reach 20% of the entire secure transmission distance. This shows that under certain channel noise conditions, the gain effect of the amplifier will be limited. After exceeding the point P (Px, Py), the gain of the optical amplifier will not only fail to further enhance the signal, but will lead to a decline in system performance. The impact of noise in the channel on the improvement ratio, such as Fig.12 As shown in the figure, when the amplification gain is fixed, the greater the noise in the channel, the more the amplification effect of the amplifier will decrease significantly. As the channel noise increases, the maximum safe distance of the system gradually decreases, resulting in a significant change in the position of Px, which in turn significantly reduces the signal enhancement area. This means that in a high-noise environment, even if an optical amplifier is used, the signal gain effect of the system is severely suppressed, affecting the overall efficiency of quantum key distribution.

[0136] In order to cope with strong channel noise, d16-DM-CVQKD can be used to effectively increase the transmission distance and improve the performance of the system in a high noise environment. This new modulation method uses phase modulation (PSK) to obtain discrete modulations of different amplitudes, thereby obtaining coherent states with different amplitudes. Especially in the case of strong channel noise, it can improve the performance of the system, such as Fig.13 and Fig.14 As shown, the situation and changing trend of 8-DM-CVQKD are basically consistent. However, under the d16-DM-CVQKD modulation mode, the Px value is closer to the maximum safe distance, and the enhanced area of ​​the optical amplifier occupies a larger proportion than the enhanced area of ​​8-DM-CVQKD, and the degraded area accounts for less than 10%. It can be concluded that in the context of adding an optical amplifier, the d16-DM-CVQKD modulation mode can more effectively utilize the gain effect of the optical amplifier and optimize the transmission performance of the system when the channel noise is strong.

[0137] In further simulation studies, more complex environmental factors, turbulence effects, light wavelength, horizontal elevation angle and other parameters were considered. Under weak turbulence intensity, visibility V = 200Km, refractive index structure constant Under strong turbulence intensity, visibility drops to V = 20 km, and the refractive index structure constant like Figure 15-17 shown.

[0138] Despite the addition of environmental factors, the impact of optical amplifiers on the key rate is consistent with the ratio of enhanced and degraded areas when environmental factors were not considered. Especially under the conditions of longer optical paths and larger channel noise, the introduction of optical amplifiers can still improve the key rate. Fig.15 or Fig.16 It can be seen that under the condition of consistent optical amplifier gain, the optical wavelength is the main factor affecting the asymptotic key rate under weak turbulence conditions. Signals with smaller wavelengths can effectively reduce signal attenuation, thereby improving the key rate. Optical signals with shorter wavelengths have lower propagation losses in the atmosphere, which is beneficial for signal transmission and reception. Therefore, under weak turbulence conditions, choosing a signal with a shorter wavelength will increase the key rate.

[0139] In addition, from Fig.15 and Fig.16 The key rate changes under different horizontal elevation angles are obtained. Under these two simulation conditions, as the horizontal elevation angle increases from 30 degrees to 90 degrees, the signal loss gradually decreases, and the geometric loss dominates in this range, which is consistent with the previous theoretical analysis conclusions.

[0140] In terms of modulation, the d16-DM-CVQKD modulation can cover the entire low-orbit satellite communication range and show good performance under different communication conditions. Under the same optical amplifier gain, the key rates are from high to low: Gaussian modulation, d16-DM-CVQKD, 8-DM-CVQKD, 4-DM-CVQKD. Gaussian modulation theoretically provides the best key rate gain, and the optical amplifier can act on the entire secure communication distance. As a discrete modulation method close to Gaussian modulation, d16-DM-CVQKD has performance close to Gaussian modulation, especially in low-orbit satellite communications, which can effectively expand the communication range and improve the key generation rate of the system.

[0141] However, in strong turbulence environments, such as Fig.17 As shown. The results under strong turbulence conditions are exactly the opposite of the trend under weak turbulence conditions. The smaller the wavelength, the lower the asymptotic key rate. In a strong turbulent environment, atmospheric turbulence has a significant impact on the propagation of light waves, which is mainly manifested in the dominant role of scattering loss per kilometer and scintillation loss. The scattering loss per kilometer comes from the fact that the size of the scattering particles in the atmosphere is comparable to the wavelength of light, causing the light wave to scatter during propagation, thereby weakening the signal intensity. The scintillation loss is due to the change in the light wavefront caused by turbulence, which causes the received signal intensity to fluctuate violently, thereby reducing the success rate of key distribution. Due to the superposition of these effects, the shorter wavelength optical signal in a strong turbulent environment exacerbates the scattering loss and scintillation loss per kilometer, ultimately leading to a significant decrease in the asymptotic key rate.

[0142] In this case, the influence of the modulation method becomes particularly prominent. The simulation results show that Gaussian modulation can maintain normal communication in a strong turbulent environment regardless of the length of the light wavelength, and can better resist the signal attenuation and fluctuation caused by turbulence. However, d16-DM-CVQKD modulation cannot communicate normally at a wavelength of 850nm, but it still maintains a high quantum key generation rate and a safe communication distance at the long wavelengths of 1550nm and 3800nm. The performance of other modulation methods has dropped significantly, especially 8-DM-CVQKD and 4-DM-CVQKD modulation. As the turbulence intensity increases, their key rates quickly drop to zero and they cannot communicate normally. This result shows that in a strong turbulent environment, the scattering and scintillation effects of light waves have a very serious impact on the quantum key distribution system. Gaussian modulation can maintain relatively good performance in such an environment, while d16-DM-CVQKD modulation can maintain normal communication by using long-wavelength quantum signals.

[0143] The simulation results show that optical amplifiers can enhance the quantum key rate in short-distance communications, especially when the vertical distance between the satellite and the ground is short. For weak turbulence intensity, the quaternary and octal discrete modulation continuous variable quantum key distribution protocols can effectively improve the key generation rate in this case, but their degradation region is large, resulting in a relatively short secure communication distance. In contrast, the use of dual-ring modulation overcomes the problems of reduced key rate and shortened security distance, and the discrete modulation method close to Gaussian modulation can give full play to the gain effect of the optical amplifier and improve the gain effect of the key rate. Changes in the turbulent environment have a significant impact on the transmission of signals. Under different turbulence intensities, the appropriate wavelength should be selected to maintain normal communication. Whether in strong or weak turbulence, the role of the optical amplifier can always increase the generation of secure keys within the working range of near-Earth satellites using Gaussian modulation and d16-DM-CVQKD modulation systems.

[0144] In an exemplary embodiment of the present disclosure, an electronic device is also provided, which may include a processor and a memory for storing executable instructions of the processor. The processor is configured to execute the steps of the method for analyzing the influence of optical amplifiers in satellite-to-ground links on quantum key distribution performance in any of the above embodiments by executing the executable instructions.

[0145] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as a system, method or program product. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software, which may be collectively referred to herein as a "circuit", "module" or "system".

[0146] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the implementation of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, including several instructions to enable a computing device (which can be a personal computer, a server, or a network device, etc.) to execute the analysis method of the influence of the optical amplifier in the satellite-to-ground link on the performance of quantum key distribution according to the implementation of the present disclosure.

[0147] In an exemplary embodiment of the present disclosure, a computer storage medium is also provided, on which a computer program is stored. When the program is executed by, for example, a processor, the steps of the method for analyzing the influence of optical amplifiers in satellite-to-ground links on quantum key distribution performance described in any of the above embodiments can be implemented.

[0148] In some possible implementations, various aspects of the present invention may also be implemented in the form of a computer program product, which includes a computer program or instructions. When the computer program product runs on a terminal device, the computer program code or instructions are used to enable the terminal device to execute the steps of various exemplary implementations of the present invention described in the above-mentioned method section of the analysis method of the impact of optical amplifiers in satellite-to-ground links on quantum key distribution performance.

[0149] The program product described above may be written in any combination of one or more programming languages ​​to perform program code for the operation of the present invention, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0150] The computer software product may be stored in a computer storage medium, which may include a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable programmable read-only memory (EEPROM), a compact disc (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

[0151] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A method for analyzing the impact of optical amplifiers on quantum key distribution performance in satellite-to-ground links, characterized in that: include: A quantum channel model for the satellite-to-ground link is constructed based on the atmospheric thickness, the vertical distance from the near-Earth satellite to the ground, the horizontal elevation angle of the ground observation station, the total distance from the near-Earth satellite to the ground observation station, and the effective distance from the observation station to the outer atmosphere. According to the satellite-to-ground link quantum channel model, a total signal loss is obtained; The total signal loss includes: geometric loss, scattering loss per kilometer and scintillation loss, wherein the geometric loss is obtained according to the vertical distance from the near-earth satellite to the ground, and the scattering loss per kilometer and scintillation loss are obtained according to the effective atmospheric thickness and atmospheric visibility; The communication sender and the communication receiver use a reverse coordination method to calculate the security key rate of the system under collective attack by a first formula; the first formula is SKR = βI(A; B) - χ Holevo (B; E), where β is the reverse regulation efficiency, I(A; B) is the mutual information between the communication sender and the communication receiver, and χ Holevo (B; E) is the upper limit of the mutual information between the communication interference party and the communication receiving party; the mutual information between the communication sending party and the communication receiving party is calculated by the noise amount associated with the modulation variance and the homodyne detection or heterodyne detection; An optical amplifier is inserted between the output end of the free space channel and the input end of the communication receiving party detection device. According to the characteristics of the optical amplifier, the corresponding transformation matrix is ​​used to describe the effect of the optical amplifier on the signal. The modulation protocol is simulated to obtain the corrected noise amount of homodyne detection and heterodyne detection, and the corrected security key rate is calculated.

2. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 1, characterized in that: The total distance from the near-Earth satellite to the ground observation station is calculated by a second formula; The second formula is: Among them, L tot is the total distance from the near-Earth satellite to the ground observation station, R is the radius of the Earth, L saz is the vertical distance from the near-Earth satellite to the ground, 3. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 2, characterized in that: The effective distance between the observation station and the outer layer of the atmosphere is calculated by the third formula; The third formula is: Among them, L atmeff is the effective atmospheric thickness, L atm is the thickness of the atmosphere, is the horizontal elevation angle of the ground observation station.

4. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 3, characterized in that: The total signal loss formula is: α tot ＝α geo +α scat ·L atmeff +α sci ； Among them, α tot is the total signal loss, α geo is the geometric loss, α scat is the scattering loss per kilometer, α sci Flicker loss.

5. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 4, characterized in that: The geometric loss formula is: Where λ is the signal wavelength, D t is the aperture diameter of the transmitting telescope, D r is the aperture diameter of the receiving telescope, T t is the transmittance of the transmitting telescope, T r is the transmittance of the receiving telescope, L p is the pointing loss efficiency, L tot ≥D r D t / λ.

6. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 5, characterized in that: The formula for the scattering loss per kilometer is: Among them, V is the atmospheric visibility, and p is the scattering index; 7. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 6, characterized in that: The flicker loss formula is: Among them, p thr is the probability threshold, is the intensity flicker index; in, is the refractive index structure constant.

8. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 1, characterized in that: The mutual information between the communication sender and the communication receiver is calculated by the fourth formula, and the upper limit of the mutual information between the communication interferer and the communication receiver is calculated by the fifth formula; The fourth formula is: Wherein, d is the detection mode parameter. When d=1, it is homodyne detection. When d=2, it is heterodyne detection. V=V A +1, V A is the modulation variance, χ tot is the total noise, ε is the channel excess noise, χ line is the total added noise of the channel in units of shot noise, χ hom / het is the amount of noise associated with homodyne or heterodyne detection, and T is the channel transmittance; The fifth formula is: Holevo (B; E) = S(ρ E )-∑ v p(y)S(ρ E / y ); Where S is the von Neumann entropy of the quantum state held by the communication interferer.

9. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 8, characterized in that: The steps of inserting an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device, using a corresponding transformation matrix to describe the effect of the optical amplifier on the signal according to the characteristics of the optical amplifier, simulating the parameters of the modulation protocol, obtaining the corrected noise amount of homodyne detection and heterodyne detection, and calculating the corrected security key rate include: Insert an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device; wherein the optical amplifier includes: a phase-sensitive amplifier and a phase-insensitive amplifier; When the optical amplifier is a phase-sensitive amplifier, the behavior of the phase-sensitive amplifier is described by a first transformation matrix, and when the optical amplifier is a phase-insensitive amplifier, the behavior of the phase-insensitive amplifier is described by a second transformation matrix; wherein the first transformation matrix is The second transformation matrix is g is the gain multiple of the optical amplifier; The M-DM-CVQKD modulation protocol, the d16-DM-CVQKD modulation protocol, and the Gaussian modulation protocol are simulated to obtain the noise amount of homodyne detection and heterodyne detection, and the Gaussian protocol correction noise amount is applied to the M-DM-CVQKD modulation protocol and the d16-DM-CVQKD modulation protocol to obtain the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount; wherein the corrected homodyne detection noise amount is calculated by the sixth formula, and the corrected heterodyne detection noise amount is calculated by the seventh formula; the sixth formula is The seventh formula is η is the detection efficiency of the detector, v el is the electrical noise, N is the inherent noise of the non-degenerate optical parametric amplifier; Substituting the corrected homodyne detection noise amount and the corrected heterodyne detection noise amount into the first formula, a corrected security key rate is obtained.

10. The method for analyzing the influence of optical amplifiers on quantum key distribution performance in satellite-to-ground links according to claim 9, characterized in that: After inserting an optical amplifier between the output end of the free space channel and the input end of the communication receiving party detection device, using a corresponding transformation matrix to describe the effect of the optical amplifier on the signal according to the characteristics of the optical amplifier, simulating the modulation protocol to obtain the corrected noise amount of homodyne detection and heterodyne detection, and calculating the corrected security key rate, the method further includes: The gain in security key rate after adding the optical amplifier is measured by the improvement ratio, and the calculation formula of the improvement ratio is: Among them, K R is the security key rate, and L is the communication distance.

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