A simulation method for satellite-machine quantum key distribution under the action of boundary layer

Abstract

The present invention provides a satellite-aircraft quantum key distribution simulation method under the action of a boundary layer, comprising: collecting photon scattering parameters to obtain wavefront information, analyzing transmission efficiency, calculating bit error rate and key rate, obtaining effective communication time and maximum communication distance, and optimizing the position of a central incident point; based on the background of satellite-aircraft quantum key distribution, the present invention studies the action mechanism of the boundary layer and quantum state characteristics, explores the quantum key distribution performance under the action of the boundary layer, proposes an optimization method for the layout of aircraft optical windows in airborne quantum secure communication, optimizes the layout of optical window positions by analyzing results such as the security key rate, and provides a feasible technical solution for the design of optical windows for airborne quantum communication.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum key distribution, and in particular to a satellite-aircraft quantum key distribution simulation optimization method under the action of a boundary layer. Background Art

[0002] Quantum key distribution can provide users with theoretically secure information and has eavesdropping detection and anti-tampering capabilities. At present, quantum secure communication networks based on ground optical fiber links and free space channels have made great progress, such as the 2000km quantum communication backbone network between Shanghai and Beijing; the intercontinental quantum communication network between multiple points on the earth with a maximum distance of 7600km; and the 460km satellite quantum communication network. Quantum satellites can effectively extend the communication distance and build an ultra-long-distance global quantum network. However, due to the characteristics of quantum satellites with fixed orbits, short communication time windows, and the fact that they can only work at night, as well as the fact that there are only a few backbone transmission links between medium and low orbit satellites and ground stations, they cannot support the full connotation of the goal of building a global wide-area secure communication system. Therefore, in order to fully open up the "peripheral nerves" of building a wide-area secure communication system and establish a mobile, on-demand, real-time coverage quantum network, it is necessary to use a more flexible airborne quantum communication system that can provide longer communication time to build the "last mile" of the quantum channel.

[0003] In 2013, Ludwig Maximilian University and the German Aerospace Center completed the first air-to-ground downlink quantum key distribution demonstration experiment, with a platform flight speed of 290km / h and a flight altitude of 1.1km. In 2020, Nanjing University proposed a quantum entanglement key distribution system based on drones, with a coverage range of 200 meters and a duration of 40 minutes. Compared with satellite-to-ground quantum communication, airborne quantum communication has the characteristics of high-speed maneuverability, all-day, and complex atmospheric working environment. It is necessary to overcome the influence of atmospheric turbulence, ambient background light, and large-scale attitude disturbances. In addition, since the surface of the aircraft is not absolutely smooth and the air is viscous, a thin layer of air with a gradually increasing flow velocity along the normal direction of the object surface appears on the surface of the high-speed flying aircraft, forming a boundary layer. When the aircraft is flying at high speed (usually greater than 0.3Ma), the generated boundary layer will adhere to the surface of the aircraft's optical communication window, producing aero-optical effects. The generation of the boundary layer distorts the incident or outgoing light, produces aiming errors, and introduces random disturbances, thereby reducing the coupling efficiency and fidelity of the quantum state. However, previous airborne quantum communication experiments only considered the effects introduced by atmospheric turbulence and molecular scattering, while ignoring the boundary layer effects.

[0004] Therefore, research on the influence of the boundary layer on the performance of quantum state transmission is still blank or just in its infancy. Studying the influence of the boundary layer on the performance of satellite-aircraft quantum key distribution is of great significance in building an airborne quantum secure communication system. Summary of the invention

[0005] The present invention aims to solve the problem of boundary layer effect in a satellite-aircraft quantum key distribution system and to provide a satellite-aircraft quantum key distribution simulation method under the effect of boundary layer to fill the gap in the prior art.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A simulation method for satellite-machine quantum key distribution under the action of a boundary layer, comprising:

[0008] Step 1: Collect the photon scattering parameters to obtain the wavefront information, that is, determine the satellite-machine quantum key distribution simulation object, and calculate the incident beam waist radius ω at the receiving end according to the various parameters in the satellite-aircraft quantum secure communication scenario. L0 , the boundary layer refractive index field n, the photon center incident point position, the satellite pitch angle and distance, and then obtain the wavefront information φ through the boundary layer rms ;

[0009] Step 2: Analyze the transmission efficiency, that is, according to the wavefront information φ rms , calculate the Snell ratio SR, and after obtaining the Snell ratio SR and the beam waist radius ω of the incident light from the receiving telescope L0 After calculating the optical path length of the photon, we calculate the ideal transmission efficiency η0 when the incident light passes through the boundary layer and illuminates the receiving telescope, and use the system receiving efficiency η caused by the components s and detector efficiency η d , the actual transmission efficiency η of photons for computer-borne quantum key distribution;

[0010] Step 3: Calculate the bit error rate and key rate to obtain the effective communication time and the farthest communication distance, that is, bring the actual total transmission efficiency η of photons in airborne quantum key distribution into the vacuum state + weak decoy state quantum key distribution protocol as the total transmission efficiency, calculate the bit error rate and key rate, and then obtain the farthest communication distance L and effective communication time t;

[0011] Step 4: Optimize the position of the central incident point, that is, the maximum communication distance L, effective communication time t, and total key length R obtained in step 3 total The performance parameters such as the center incident point position are used as feedback to optimize the geometric center position of the airborne receiving telescope.

[0012] Furthermore,

[0013] Step 1 includes:

[0014] Step 1-1: Get the effective beam waist of photons to the receiving end of the aircraft;

[0015] Step 1-2: Get the boundary layer refractive index field;

[0016] Step 1-3: Establish a spherical coordinate system with the geometric center of the airborne receiving telescope as the origin;

[0017] Step 1-4: Divide the boundary layer refractive index field into sub-units and calculate the optical path of the photon to obtain the wavefront difference of the photon;

[0018] Step 2 includes:

[0019] Step 2-1: Calculate the Sternel ratio;

[0020] Step 2-2: Calculate the ideal transmission efficiency of the light beam when it passes through the boundary layer and illuminates the receiving telescope;

[0021] Step 2-3: Calculate the total efficiency of actual photon transmission in the satellite-aircraft quantum key distribution system;

[0022] Step 3 includes:

[0023] Step 3-1: Determine the basic parameters in the vacuum state + weak decoy state quantum key distribution protocol;

[0024] Step 3-2: Calculate the bit error rate and key rate to obtain the total key length;

[0025] Step 3-3: Get the effective communication time and the maximum communication distance.

[0026] Furthermore,

[0027] In step 1-1, according to the actual downlink in the satellite-aircraft quantum secure communication scenario, the effective beam waist ω of the photon to the aircraft receiving end L0 for:

[0028]

[0029] where σ Τ is the pointing error of the satellite transmitting end telescope, l is the photon transmission distance, ω L Receive beam waist for aircraft without considering pointing error:

[0030]

[0031] Where λ is the wavelength of light, θ is the zenith angle of the receiving telescope, and D T is the diameter of the transmitting telescope, r0 is the field coefficient related to the zenith angle, ω0 is the waist radius of the transmitted Gaussian beam;

[0032] ω0=0.316D T (3)

[0033] In step 1-2, the aircraft is meshed according to its shape, and then the aircraft's speed, direction, altitude, ambient air density, and meshed data are imported into the fluid calculation software. The boundary layer density field ρ in this state is calculated, and the boundary layer refractive index field n is calculated using the Gladstone-Dale equation:

[0034] n=1+ρK GD (4)

[0035] Where K GD is the GD (Gladstone-Dale) constant, in m 3 / kg,K GD It complies with the following empirical formula:

[0036]

[0037] In step 1-3, the airborne receiving end telescope is conformally installed on the upper surface of the nose (without changing the original shape of the aircraft), and its geometric center is located on the symmetry axis of the upper surface of the aircraft. The projection distance between the geometric center point of the airborne receiving end telescope and the tip point of the nose along the flight direction of the aircraft is recorded as X0. A spherical coordinate system is established with the geometric center of the airborne receiving end telescope as the origin O. The x-axis is parallel to the tangent direction of the meridian and points to the true north. The z-axis coincides with the local vertical line and points to the zenith. The y-axis, x-axis and z-axis form a right-handed coordinate system. The distance from the origin to the satellite point S is recorded as d. The angle between the projection line of OS on the xoy plane and the positive direction of the x-axis is the azimuth angle α, and the angle between the projection line of OS on the xoy plane and OS is the pitch angle β. The satellite ephemeris and the aircraft track data are converted into coordinates and calculated and brought into the spherical coordinate system to obtain the data of the azimuth angle α, pitch angle β and distance d of the satellite to the aircraft changing with time in the coordinate system;

[0038] In steps 1-4, the three-dimensional boundary layer refractive index field is uniformly divided into multiple refractive index cube units. The interpolation method based on polynomial fitting is combined with the Adams linear multi-step method. The pitch angle and distance data are used for ray tracing. By integrating the refractive index n along the propagation path P, the optical path length OPL of the photon is calculated:

[0039] OPL(x,y,t)=∫ P n(x,y,z,t)dp (6)

[0040] Where n(x,y,z,t) represents the refractive index at (x,y,z) in the new coordinate system at time t, P represents the light propagation path; the relative value of OPL, that is, the optical path difference OPD, is defined as:

[0041]

[0042] in Represents the average value of the optical path in space;

[0043] The wavefront difference of the photon φ rms Defined as:

[0044]

[0045] OPD rms It represents the spatial RMS value of OPD at the optical aperture of the receiving end;

[0046] In step 2-1, the Sternel ratio (SR) is the light intensity I at the receiving end. r Divided by the light intensity I0 at the transmitting end, according to the wavefront information φ rms , approximate calculation of the Sternel ratio

[0047]

[0048] In step 2-2, the Sternel ratio SR and the beam waist radius ω of the incident light of the receiving telescope are used. L0 , calculate the ideal transmission efficiency η0 when the light beam passes through the boundary layer and illuminates the receiving telescope

[0049]

[0050] Among them, D R is the diameter of the receiving telescope, is the extinction optical thickness;

[0051] The system receiving efficiency η caused by the components used in step 2-3 s and detector efficiency η d , calculate the total efficiency η of actual photon transmission in the satellite-aircraft quantum key distribution system;

[0052] η=η0η s η d (11)

[0053] The total loss of actual photon transmission is -10lg(η);

[0054] The basic parameters in the vacuum state + weak decoy state quantum key distribution protocol in step 3-1 include: signal state intensity μ, decoy state intensity ν, system repetition frequency N, signal state probability P s , the probability of decoy state P d ;

[0055] In step 3-2, the actual total transmission efficiency η of photons in airborne quantum key distribution is brought into the vacuum state + weak decoy state quantum key distribution protocol, and the key rate R is calculated as:

[0056] R ≥ q{Q1[1-H2(e1)]-Q μ f(E μ )H2(E μ )}P s N (12)

[0057] Where f(x) is the error correction efficiency of the classical error correction code, q represents the basis vector comparison efficiency. In the BB84 system of balanced basis vectors, the probability of selecting two basis vectors is the same, then q = 1 / 2; Q μ represents the total count rate in the signal state, E μ represents the bit error rate in the signal state, Q1 represents the single photon count rate in the signal state, e1 represents the single photon error rate, and H2(x) is the binary Shannon entropy function:

[0058] H2(x)=-xlog(x)-(1-x)log(1-x) (13)

[0059] Total count rate Q in signal state μ It is expressed as:

[0060] Q μ =Y0+1-e -ημ (14)

[0061] Where Y0 is the response rate of the vacuum state in the quantum key distribution system, η is the total efficiency of photon transmission, μ is the signal state intensity, then the signal state bit error rate E μ Q μ for:

[0062] E μ Q μ =e0Y0+e d (1-e -ημ ) (15)

[0063] Where e0 is the bit error caused by vacuum, e d =1% is the probability of a photon hitting the wrong detector;

[0064] Bit error rate E in signal state μ for:

[0065] E μ =E μ Q μ / Q μ (16)

[0066] The single photon counting rate Q1 in the signal state is:

[0067]

[0068] Where L represents its lower bound, Qν represents the total count rate in the decoy state; the single photon bit error rate e1 is:

[0069]

[0070]

[0071] Deception bit error rate E ν Q ν for:

[0072] E ν Q ν =e0Y0+e d (1-e -ην ) (20)

[0073] In step 3-3, the effective communication time t is the time interval corresponding to when the key rate is greater than zero; the maximum communication distance L is the maximum distance that can be reached between the communication objects within the effective communication time.

[0074] Furthermore,

[0075] The satellite object in the satellite-machine quantum key distribution simulation object is the Micius quantum science experimental satellite; the aircraft object is the DLR-F6 wing-body assembly, with a length of 1.17 meters;

[0076] Step 1-1 Τ =10μrad,λ=1550mm,D T =0.3m, r0=0.4m;

[0077] In step 1-2, the aircraft is flying at a constant speed of 0.7 Ma from south to north, at an altitude of 10 kilometers, and the ambient air density is 0.41271 kg / m 3 , the fluid calculation software is ANSYS Fluent;

[0078] In step 1-3, X0 should avoid the cockpit position at the nose of the aircraft; the aircraft is located at 34.265637N, 108.953489E at t=0, i.e. 00:23:41 on May 30, 2022, China Standard Time, at an altitude of 10km and flying at a constant speed from south to north;

[0079] The three-dimensional boundary layer refractive index field in steps 1-4 is uniformly divided into 10 9 Index cube units;

[0080] Step 2-2D R =0.5m,

[0081] System receiving efficiency η caused by components in step 2-3 s =60%, detector efficiency ηd =15%,

[0082] In step 3-1, the signal state strength μ = 0.8, the decoy state strength ν = 0.1, the system repetition frequency N = 100 MHz, and the signal state probability P s =50%, the probability of deception state P d =25%.

[0083] Furthermore,

[0084] When the distance between the geometric center of the airborne receiving end and the projection of the nose top is X0=66mm, the effective communication time is reduced to 280s under the influence of the boundary layer, and the maximum communication distance is reduced to 1163km. The total key length R is obtained by integrating the key rate with the communication time. total 6.84×10 5 bit.

[0085] Furthermore,

[0086] When the distance between the geometric center of the airborne receiving end and the projection of the nose top is X0=83mm, the effective communication time is reduced to 290s under the influence of the boundary layer, and the maximum communication distance is reduced to 1226km. The total key length R is obtained by integrating the key rate with the communication time. total 7.51×10 5 bit.

[0087] Furthermore,

[0088] In the satellite-machine quantum key distribution simulation object, the satellite object is a quantum communication satellite, and the aircraft object is an aircraft equipped with a quantum communication receiver.

[0089] Compared with the prior art, the advantages of the present invention are: based on the background of satellite-aircraft quantum key distribution, the present invention studies the action mechanism of the boundary layer and quantum state characteristics, explores the quantum key distribution performance under the action of the boundary layer, and proposes an optimization method for the layout of aircraft optical windows in airborne quantum secure communication. By analyzing the results such as the security key rate, the optical window position layout is optimized, which provides a feasible technical solution for the optical window design of airborne quantum communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below.

[0091] Figure 1 is a flow chart of the method of the present invention;

[0092] Figure 2 It is a schematic diagram of the geometric center position of the telescope at the airborne receiving end and the projection distance from the top of the nose;

[0093] Figure 3 This is a diagram of the satellite-aircraft quantum key distribution scenario;

[0094] Figure 4 It is a graph showing the satellite's azimuth, pitch angle and distance to the aircraft changing over time;

[0095] Figure 5 It is the curve of photon transmission loss, bit error rate and key rate changing with time when the distance between the geometric center of the airborne receiving end and the projection of the nose is 66mm with or without boundary layer;

[0096] Figure 6 It is the curve of photon transmission loss, bit error rate and key rate changing with time when the geometric center position of the airborne receiving end and the projection distance of the nose are 83mm with or without boundary layer. DETAILED DESCRIPTION

[0097] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention.

[0098] The DLR-F6 wing-body assembly is a small-size model of a typical cruise configuration of a modern transport aircraft developed by the German Aerospace Center, with a length of 1.17 meters. This model is one of the standard examples used in the second and third drag prediction seminars of the American Institute of Aeronautics and Astronautics, and there are many simulation and experimental results for reference. Therefore, the present invention selects the DLR-F6 wing-body assembly model as the aircraft object in this embodiment. In addition, the world's first space quantum science experimental satellite independently developed by my country, the Mozi quantum science experimental satellite, is selected as the satellite object in this embodiment.

[0099] like Figure 1 As shown, this embodiment discloses a simulation method for star-machine quantum key distribution under the action of a boundary layer, comprising the following steps:

[0100] Step 1: Collect photon scattering parameters to obtain wavefront information.

[0101] Step 1-1: Get the effective beam waist of the photon to the aircraft receiving end. According to the actual downlink in the satellite-aircraft quantum secure communication scenario, the effective beam waist of the photon to the aircraft receiving end ω L0 It can be expressed as:

[0102]

[0103] where σ Τ =10μrad is the pointing error of the satellite transmitter telescope, l is the photon transmission distance, ω LReceive beam waist for aircraft without considering pointing error:

[0104]

[0105] Where λ = 1550 mm is the wavelength of light, θ is the zenith angle of the receiving telescope, and D T =0.3m is the diameter of the transmitting telescope, r0=0.4m is the field coefficient related to the zenith angle, and ω0 is the waist radius of the transmitted Gaussian beam.

[0106] ω0=0.316D T (3)

[0107] Step 1-2: Get the boundary layer refractive index field. According to the operating state of the aircraft in the satellite-aircraft quantum secure communication scenario, assume that the aircraft is flying at a constant speed of 0.7 Ma from south to north, at an altitude of 10 kilometers, and the ambient air density is 0.41271 kg / m 3 The aircraft is meshed according to its shape, and the above state parameters and the meshed data are imported into the fluid calculation software ANSYS Fluent. The boundary layer density field ρ under this state can be obtained by calculation, and the boundary layer refractive index field n is calculated using the Gladstone-Dale equation:

[0108] n=1+ρK GD (4)

[0109] Where K GD is the GD (Gladstone-Dale) constant, in m 3 / kg, generally speaking, K GD It also complies with the following empirical formula, namely:

[0110]

[0111] Among them, λ=1550mm is the wavelength.

[0112] Step 1-3: Establish a spherical coordinate system with the geometric center of the airborne receiving telescope as the origin. The airborne receiving telescope is conformally mounted on the upper surface of the aircraft nose (without changing the original shape of the aircraft), and its geometric center is located on the symmetry axis of the upper surface of the aircraft. The projection distance between the geometric center point of the airborne receiving telescope and the tip of the aircraft nose along the flight direction of the aircraft is recorded as X0, as follows: Figure 2As shown. In order to avoid the cockpit position at the nose, X0 should be greater than 37mm, assuming X0 = 66mm. A spherical coordinate system is established with the geometric center of the airborne receiving telescope as the origin O. The x-axis is parallel to the tangent direction of the meridian and points to the north. The z-axis coincides with the local vertical and points to the zenith. The y-axis, x-axis and z-axis form a right-handed coordinate system. The distance from the origin to the satellite point S is denoted as d, the angle between the projection line of OS on the xoy plane and the positive direction of the x-axis is the azimuth angle α, and the angle between the projection line of OS on the xoy plane and OS is the pitch angle β, as shown Figure 3 shown.

[0113] Assume that the aircraft is located at (34.265637N, 108.953489E, 10km) at t=0 (China Standard Time May 30, 2022 00:23:41) and flies at a constant speed from south to north. The satellite ephemeris and aircraft track data are converted into coordinates and then brought into the spherical coordinate system to obtain the data of the satellite's azimuth angle α, pitch angle β and distance d to the aircraft over time in the coordinate system, as shown in Figure 4 As shown, the horizontal axis is the communication time t, Figure 4 The solid line in the figure above represents the satellite's azimuth, and the dotted line represents the satellite's elevation. Figure 4 The vertical axis in the figure below represents the distance d between the satellite and the aircraft.

[0114] Step 1-4: Divide the boundary layer refractive index field into sub-units and calculate the optical path length of the photon to obtain the wavefront difference of the photon. 9 The refractive index cube unit is used, and the interpolation method based on polynomial fitting is combined with the Adams linear multi-step method. The pitch angle and distance data are used for ray tracing. The optical path OPL of the photon is calculated by integrating the refractive index n along the propagation path P:

[0115] OPL(x,y,t)=∫ P n(x,y,z,t)dp (6)

[0116] Where n(x,y,z,t) represents the refractive index at (x,y,z) in the new coordinate system at time t, and P represents the light propagation path. The relative value of OPL, that is, the optical path difference OPD, is defined as:

[0117]

[0118] in Represents the average value of the optical path in space;

[0119] The wavefront difference of the photon φ rms It can be defined as:

[0120]

[0121] OPD rms It represents the spatial RMS value of OPD at the optical aperture of the receiving end.

[0122] Step 2: Analyze the transmission efficiency.

[0123] Step 2-1: Calculate the Snell ratio. The Snell ratio (SR) is the light intensity I at the receiving end. r Divided by the light intensity I0 at the transmitting end, according to the wavefront information φ rms , we can approximate the Sternel ratio

[0124]

[0125] In good atmospheric conditions and at low flight speeds (usually ), airborne quantum communication will be carried out without the influence of the boundary layer, and SR≈1.0.

[0126] Step 2-2: Calculate the ideal transmission efficiency of the light beam when it passes through the boundary layer and illuminates the receiving telescope. Use the Sternel ratio SR and the beam waist radius ω of the incident light at the receiving telescope L0 , calculate the ideal transmission efficiency η0 when the light beam passes through the boundary layer and illuminates the receiving telescope

[0127]

[0128] Among them, D R =0.5m is the diameter of the receiving telescope, is the extinction optical thickness.

[0129] Step 2-3: Calculate the total efficiency of actual photon transmission in the satellite-aircraft quantum key distribution system. Use the system receiving efficiency η caused by components s =60% and detector efficiency η d =15%, calculate the actual total photon transmission efficiency η of the satellite-aircraft quantum key distribution system.

[0130] η=η0η s η d (11)

[0131] The actual total loss of photon transmission is -10lg(η).

[0132] Step 3: Calculate the bit error rate and key rate.

[0133] Step 3-1: Determine the basic parameters in the vacuum state + weak decoy state quantum key distribution protocol. The signal state strength μ = 0.8, the decoy state strength ν = 0.1, the system repetition frequency N = 100MHz, the signal state probability P s =50%, the probability of deception state Pd =25%.

[0134] Step 3-2: Calculate the bit error rate and key rate, and then get the total key length. Bring the actual total transmission efficiency η of photons in airborne quantum key distribution into the vacuum state + weak decoy state quantum key distribution protocol, and the key rate R is calculated as:

[0135] R ≥ q{Q1[1-H2(e1)]-Q μ f(E μ )H2(E μ )}P s N (12)

[0136] Where f(x) is the error correction efficiency of the classical error correction code, q represents the basis vector comparison efficiency, and in the BB84 system of balanced basis vectors, the probability of selecting the two basis vectors is the same, then q = 1 / 2. μ represents the total count rate in the signal state, E μ represents the bit error rate in the signal state, Q1 represents the single photon count rate in the signal state, e1 represents the single photon error rate, and H2(x) is the binary Shannon entropy function:

[0137] H2(x)=-xlog(x)-(1-x)log(1-x) (13)

[0138] Total count rate Q in signal state μ It can be expressed as:

[0139] Q μ =Y0+1-e -ημ (14)

[0140] Where Y0 is the response rate of the vacuum state in the quantum key distribution system, η is the total efficiency of photon transmission, and μ is the signal state intensity. Then the signal state bit error rate E μ Q μ It can be calculated as:

[0141] E μ Q μ =e0Y0+e d (1-e -ημ ) (15)

[0142] Where e0 is the bit error caused by vacuum, usually equal to 0.5, e d =1% is the probability of a photon hitting the wrong detector.

[0143] So the bit error rate E under the signal state μ for:

[0144] E μ =E μ Q μ / Qμ (16)

[0145] The single photon counting rate Q1 in the signal state is:

[0146]

[0147] Where L represents its lower bound, Q ν represents the total count rate in the decoy state. The single photon bit error rate e1 can be calculated as:

[0148]

[0149]

[0150] Then the decoy bit error rate E ν Q ν It can be calculated as:

[0151] E ν Q ν =e0Y0+e d (1-e -ην ) (20)

[0152] Step 3-3: Get the effective communication time and the maximum communication distance. The effective communication time t is the time interval corresponding to when the key rate is greater than zero; the maximum communication distance L is the maximum distance that can be reached between the communication objects within the effective communication time;

[0153] according to Figure 4 The satellite's azimuth angle α, pitch angle β and distance d to the aircraft change over time, and the effective communication time t and the maximum communication distance L are obtained.

[0154] Step 4: Optimize the position of the central incident point. That is, the maximum communication distance L, effective communication time t, and total key length R obtained in step 3 are total The performance parameters such as the center incident point position are used as feedback to optimize the geometric center position of the airborne receiving telescope.

[0155] When the distance between the geometric center of the airborne receiving end and the projection of the top of the nose is X0 = 66 mm, the actual total transmission loss of photons, the bit error rate and the key rate in this scenario are calculated as follows: Figure 5 As shown, the solid line is the control result without the boundary layer, the dotted line is the result obtained under the influence of the boundary layer, the ordinate represents the total loss of actual photon transmission, the bit error rate and the key rate, and the abscissa represents the communication time. It can be seen that the boundary layer has a certain impact on the communication performance: increasing the photon transmission loss, reducing the maximum communication distance, reducing the effective communication time, increasing the bit error rate, and reducing the key rate. Under the influence of the boundary layer, the effective communication time is reduced to 280s, that is, Figure 5In the bottom graph, from 80 seconds to 360 seconds, the maximum communication distance is reduced to 1163 km, corresponding to Figure 4 The following figure shows the key rate from 80 seconds to 360 seconds. Integrate the key rate over the communication time to get the total key length R total 6.84×10 5 bit.

[0156] When the distance between the geometric center of the airborne receiving end and the projection of the top of the nose is X0=83mm, the actual total transmission loss of photons, the bit error rate and the key rate in this scenario are calculated as follows: Figure 6 As shown, the solid line is the control result without the boundary layer, the dotted line is the result obtained under the influence of the boundary layer, the ordinate represents the total loss of actual photon transmission, the bit error rate and the key rate, and the abscissa represents the communication time. It can be seen that the boundary layer has a certain impact on the communication performance: increasing the photon transmission loss, reducing the maximum communication distance, reducing the effective communication time, increasing the bit error rate, and reducing the key rate. Under the influence of the boundary layer, the effective communication time is reduced to 290s, that is, Figure 5 In the bottom graph, from 80 seconds to 370 seconds, the maximum communication distance is reduced to 1226 km, corresponding to Figure 4 The following figure shows the key rate from 80 seconds to 370 seconds. Integrating the key rate over the communication time gives the total key length R total 7.51×10 5 bit. It shows that the geometric center position of the receiving end and the projection distance of the nose are 83mm, which is better. By changing the parameter X0 and comparing the calculation results, the geometric center position of the telescope of the airborne receiving end can be continuously optimized. Similarly, the method of the present invention can also be used on an actual aircraft to obtain the optimal geometric center position.

[0157] In this embodiment, the density field of the aircraft boundary layer is obtained through simulation calculation, and the Adams linear multi-step method is used for ray tracing to obtain the transmission efficiency of photons, and then the bit error rate and key rate are obtained. The existing technology has not yet involved the field related to satellite-to-aircraft quantum key distribution. The proposed method can provide method support for air-to-space high-fidelity quantum state transmission.

[0158] In this embodiment, the key distribution performance data is used as a feedback parameter. By comparing parameters such as the maximum communication distance, the effective communication time, and the total key length, the position of the central incident point (the geometric center of the airborne receiving telescope) is optimized, thereby providing a feasible technical solution for the airborne optical window layout.

Claims

1. A simulation method for satellite-machine quantum key distribution under the action of a boundary layer, comprising: Step 1: Collect the photon scattering parameters to obtain the wavefront information, that is, determine the satellite-machine quantum key distribution simulation object, and calculate the incident beam waist radius ω at the receiving end according to the various parameters in the satellite-aircraft quantum secure communication scenario. L0 , the boundary layer refractive index field n, the photon center incident point position, the satellite pitch angle and distance, and then obtain the wavefront information φ through the boundary layer rms ; Step 1 includes: Step 1-1: Get the effective beam waist of photons to the receiving end of the aircraft; Step 1-2: Get the boundary layer refractive index field; Step 1-3: Establish a spherical coordinate system with the geometric center of the airborne receiving telescope as the origin; Step 1-4: Divide the boundary layer refractive index field into sub-units and calculate the optical path of the photon to obtain the wavefront difference of the photon; Step 2: Analyze the transmission efficiency, that is, according to the wavefront information φ rms , calculate the Snell ratio SR, and after obtaining the Snell ratio SR and the beam waist radius ω of the incident light from the receiving telescope L0 After calculating the optical path length of the photon, we calculate the ideal transmission efficiency η0 when the incident light passes through the boundary layer and illuminates the receiving telescope, and use the system receiving efficiency η caused by the components s and detector efficiency η d , the actual transmission efficiency η of photons for computer-borne quantum key distribution; Step 2 includes: Step 2-1: Calculate the Sternel ratio; Step 2-2: Calculate the ideal transmission efficiency of the light beam when it passes through the boundary layer and illuminates the receiving telescope; Step 2-3: Calculate the total efficiency of actual photon transmission in the satellite-aircraft quantum key distribution system; Step 3: Calculate the bit error rate and key rate to obtain the effective communication time and the farthest communication distance, that is, bring the actual total transmission efficiency η of photons in airborne quantum key distribution into the vacuum state + weak decoy state quantum key distribution protocol as the total transmission efficiency, calculate the bit error rate and key rate, and then obtain the farthest communication distance L and effective communication time t; Step 3 includes: Step 3-1: Determine the basic parameters in the vacuum state + weak decoy state quantum key distribution protocol; Step 3-2: Calculate the bit error rate and key rate to obtain the total key length; Step 3-3: Get the effective communication time and the maximum communication distance; Step 4: Optimize the position of the central incident point, that is, the maximum communication distance L, effective communication time t, and total key length R obtained in step 3 total As feedback of the central incident point position, the geometric center position of the airborne receiving telescope is optimized.

2. The method for simulating satellite-machine quantum key distribution under the action of a boundary layer as claimed in claim 1, characterized in that: In step 1-1, according to the actual downlink in the satellite-aircraft quantum secure communication scenario, the effective beam waist ω of the photon to the aircraft receiving end L0 for: where σ Τ is the pointing error of the satellite transmitting end telescope, l is the photon transmission distance, ω L Receive beam waist for aircraft without considering pointing error: Where λ is the wavelength of light, θ is the zenith angle of the receiving telescope, and D T is the diameter of the transmitting telescope, r0 is the field coefficient related to the zenith angle, ω0 is the waist radius of the transmitted Gaussian beam; ω0=0.316D T (3) In step 1-2, the aircraft is meshed according to its shape, and then the aircraft's speed, direction, altitude, ambient air density, and meshed data are imported into the fluid calculation software. The boundary layer density field ρ in this state is calculated, and the boundary layer refractive index field n is calculated using the Gladstone-Dale equation: n=1+ρK GD (4) Where K GD is the GD (Gladstone-Dale) constant, in m 3 / kg,K GD It complies with the following empirical formula: In step 1-3, the airborne receiving end telescope is conformally installed on the upper surface of the nose, and its geometric center is located on the symmetry axis of the upper surface of the aircraft. The projection distance between the geometric center point of the airborne receiving end telescope and the tip point of the nose along the flight direction of the aircraft is recorded as X0. A spherical coordinate system is established with the geometric center of the airborne receiving end telescope as the origin O. The x-axis is parallel to the tangent direction of the meridian and points to the true north. The z-axis coincides with the local vertical line and points to the zenith. The y-axis, the x-axis and the z-axis form a right-handed coordinate system. The distance from the origin to the satellite point S is recorded as d. The angle between the projection line of OS on the xoy plane and the positive direction of the x-axis is the azimuth angle α, and the angle between the projection line of OS on the xoy plane and OS is the pitch angle β. The satellite ephemeris and the aircraft track data are converted into coordinates and other calculations and brought into the spherical coordinate system to obtain the data of the azimuth angle α, pitch angle β and distance d of the satellite to the aircraft changing with time in the coordinate system; In steps 1-4, the three-dimensional boundary layer refractive index field is uniformly divided into multiple refractive index cube units. The interpolation method based on polynomial fitting is combined with the Adams linear multi-step method. The pitch angle and distance data are used for ray tracing. By integrating the refractive index n along the propagation path P, the optical path length OPL of the photon is calculated: OPL(x,y,t)=∫ P n(x,y,z,t)dp (6) Where n(x,y,z,t) represents the refractive index at (x,y,z) in the new coordinate system at time t, P represents the light propagation path; the relative value of OPL, that is, the optical path difference OPD, is defined as: in Represents the average value of the optical path in space; The wavefront difference of the photon φ rms Defined as: OPD rms It represents the spatial RMS value of OPD at the optical aperture of the receiving end; In step 2-1, the Sternel ratio (SR) is the light intensity I at the receiving end. r Divided by the light intensity I0 at the transmitting end, according to the wavefront information φ rms , approximate calculation of the Sternel ratio In step 2-2, the Sternel ratio SR and the beam waist radius ω of the incident light of the receiving telescope are used. L0 , calculate the ideal transmission efficiency η0 when the light beam passes through the boundary layer and illuminates the receiving telescope Among them, D R is the diameter of the receiving telescope, is the extinction optical thickness; The system receiving efficiency η caused by the components used in step 2-3 s and detector efficiency η d , calculate the total efficiency η of actual photon transmission in the satellite-aircraft quantum key distribution system; η=η0η s or d (11) The total loss of actual photon transmission is -10lg(η); The basic parameters in the vacuum state + weak decoy state quantum key distribution protocol in step 3-1 include: signal state intensity μ, decoy state intensity ν, system repetition frequency N, signal state probability P s , the probability of decoy state P d ; In step 3-2, the actual total transmission efficiency η of photons in airborne quantum key distribution is brought into the vacuum state + weak decoy state quantum key distribution protocol, and the key rate R is calculated as: R≥q{Q1[1-H2(e1)]-Q μ f(E μ )H2(E μ )}P s N (12) Where f(x) is the error correction efficiency of the classical error correction code, q represents the basis vector comparison efficiency. In the BB84 system of balanced basis vectors, the probability of selecting two basis vectors is the same, then q = 1 / 2; Q μ represents the total count rate in the signal state, E μ represents the bit error rate in the signal state, Q1 represents the single photon count rate in the signal state, e1 represents the single photon error rate, and H2(x) is the binary Shannon entropy function: H2(x)=-xlog(x)-(1-x)log(1-x) (13) Total count rate Q in signal state μ It is expressed as: Q μ =Y0+1-e -ημ (14) Where Y0 is the response rate of the vacuum state in the quantum key distribution system, η is the total efficiency of photon transmission, μ is the signal state intensity, then the signal state bit error rate E μ Q μ for: AND μ Q μ =e0Y0+e d (1-e -ημ ) (15) Where e0 is the bit error caused by vacuum, e d =1% is the probability of a photon hitting the wrong detector; The bit error rate E in the signal state μ for: E μ =E μ Q μ / Q μ (16) The single photon counting rate Q1 in the signal state is: Where L represents its lower limit, Q ν represents the total count rate in the decoy state; the single photon bit error rate e1 is: Deception bit error rate E ν Q ν for: AND ν Q ν =e0Y0+e d (1-e -ην ) (20) In step 3-3, the effective communication time t is the time interval corresponding to when the key rate is greater than zero; the maximum communication distance L is the maximum distance that can be reached between the communication objects within the effective communication time.

3. The method for simulating satellite-machine quantum key distribution under the action of a boundary layer as claimed in claim 2, characterized in that: The satellite object in the satellite-machine quantum key distribution simulation object is the Micius quantum science experimental satellite; the aircraft object is the DLR-F6 wing-body assembly, with a length of 1.17 meters; Step 1-1 Τ =10μrad,λ=1550mm,D T =0.3m, r0=0.4m; In step 1-2, the aircraft is flying at a constant speed of 0.7 Ma from south to north, at an altitude of 10 kilometers, and the ambient air density is 0.41271 kg / m 3 , the fluid calculation software is ANSYS Fluent; In step 1-3, X0 should avoid the cockpit position at the nose of the aircraft; the aircraft is located at 34.265637N, 108.953489E at t=0, i.e. 00:23:41 on May 30, 2022, China Standard Time, at an altitude of 10km and flying at a constant speed from south to north; The three-dimensional boundary layer refractive index field in steps 1-4 is uniformly divided into 10 9 Index cube units; Step 2-2D R =0.5m, System receiving efficiency η caused by components in step 2-3 s =60%, detector efficiency η d =15%, In step 3-1, the signal state strength μ = 0.8, the decoy state strength ν = 0.1, the system repetition frequency N = 100 MHz, and the signal state probability P s =50%, the probability of deception state P d =25%.

4. The method for simulating satellite-machine quantum key distribution under the action of a boundary layer as claimed in claim 3, characterized in that: When the distance between the geometric center of the airborne receiving end and the projection of the nose top is X0=66mm, the effective communication time is reduced to 280s under the influence of the boundary layer, and the maximum communication distance is reduced to 1163km. The total key length R is obtained by integrating the key rate with the communication time. total 6.84×10 5 bit.

5. The method for simulating satellite-machine quantum key distribution under the action of a boundary layer as claimed in claim 4, characterized in that: When the distance between the geometric center of the airborne receiving end and the projection of the nose top is X0=83mm, the effective communication time is reduced to 290s under the influence of the boundary layer, and the maximum communication distance is reduced to 1226km. The total key length R is obtained by integrating the key rate with the communication time. total 7.51×10 5 bit.

6. A method for simulating satellite-machine quantum key distribution under the action of a boundary layer as claimed in any one of claims 1 to 5, characterized in that: In the satellite-machine quantum key distribution simulation object, the satellite object is a quantum communication satellite, and the aircraft object is an aircraft equipped with a quantum communication receiver.

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