CN109361505B - Improved method for free space quantum channel performance - Google Patents

Improved method for free space quantum channel performance Download PDF

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CN109361505B
CN109361505B CN201811096509.5A CN201811096509A CN109361505B CN 109361505 B CN109361505 B CN 109361505B CN 201811096509 A CN201811096509 A CN 201811096509A CN 109361505 B CN109361505 B CN 109361505B
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single photon
receiving terminal
turbulence
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CN109361505A (en
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车志刚
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Shaanxi Aerospace Technology Development Co., Ltd. west blue
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/11—Arrangements specific to free-space transmission, i.e. transmission through air or vacuum
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/70—Photonic quantum communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H04B17/3912—Simulation models, e.g. distribution of spectral power density or received signal strength indicator [RSSI] for a given geographic region

Abstract

The invention relates to an improved method for free space quantum channel performance, comprising the steps of: a sending terminal of a ground station emits single photon pulses, and the single photon pulses firstly pass through the atmosphere and then are transmitted to a satellite receiving terminal; the satellite receiving end reflects the obtained single photon pulse to a receiving terminal of the ground station, the receiving terminal receives signals by adopting a single photon detector to obtain energy hv, and the energy hv triggers a counter to work and simultaneously counts the single photons. The invention provides a single photon receiving efficiency model under the condition of different intensity atmospheric turbulence interference, and in addition, a receiving terminal can ensure higher single photon receiving rate by selecting a proper antenna aperture.

Description

Improved method for free space quantum channel performance
Technical Field
The invention belongs to the field of communication, and particularly relates to an improvement method for the performance of a free space quantum channel.
Background
In the transmission process of the single photon in the free space quantum communication channel, the transmission distance is limited by obstacles such as atmospheric environment, experimental equipment and the like. The most critical problems are the beam drift, broadening and deformation caused by atmospheric turbulence and the stability guarantee of the optical system to the transmission of the single photon beam in the external environment. Meanwhile, single photon beams are also geographically constrained (curvature, terrain, obstacles, etc.) on earth during transmission, as well as absorption of radiation from sub-atmospheric layers. Atmospheric turbulence, a major form of atmospheric motion, is a major obstacle to the transport of single photons in free space.
Quantum communication can be divided into two broad categories, i.e., fiber optic communication and free space quantum communication, depending on the transmission channel. Due to noise interference at the end of the single photon detector and link loss of the single photon in the transmission process of the quantum channel, the farthest transmission distance of optical fiber communication is greatly limited. Because the effective thickness of the atmosphere is about 5-10km, the energy attenuation of a single photon in the outer space transmission process is approximately 0. Therefore, free space quantum communication is the best choice to achieve global quantum communication.
Disclosure of Invention
In order to solve the problems in the prior art, the invention discloses an improvement method for the performance of a free space quantum channel, which provides a single photon receiving efficiency model under the conditions of different intensity atmospheric turbulence interference, and a receiving terminal selects a proper antenna aperture to ensure higher single photon receiving rate.
A method for improving the performance of a free-space quantum channel, comprising the steps of:
a sending terminal of a ground station emits single photon pulses, and the single photon pulses firstly pass through the atmosphere and then are transmitted to a satellite receiving terminal;
the satellite receiving terminal reflects the obtained single photon pulse to a receiving terminal of the ground station, the receiving terminal receives signals by adopting a single photon detector to obtain energy hv, and the energy hv triggers a counter to work and simultaneously counts single photons;
at time intervals t0,t0+T]In the method, the probability p (n) that the receiving terminal counts n single photons can be expressed as
Figure BDA0001805671320000021
Wherein q is the average number of single photons and can be expressed as
Figure BDA0001805671320000022
Here, p represents the single photon reception efficiency of the receiving terminal, T is the interval of optoelectronics, and i (T) refers to the field strength of the receiving terminal, where T0 represents a certain point in time.
In a preferred embodiment of the present invention, the receiving terminal single photon reception efficiency p is defined as:
p＝pacq×K (3)
wherein p isacqThe single photon capture rate of the aperture of the telescope antenna is shown, and K represents the efficiency of the optical pulse signal to penetrate through the atmospheric turbulence, namely the fluctuation intensity transmittance of the single photon pulse.
In a preferred embodiment of the invention, the single photon capture rate of the telescope antenna aperture can be expressed as:
Figure BDA0001805671320000023
wherein a represents the antenna aperture of the receiving end telescope, L is the transmission distance between the single photon emission end and the satellite receiving end, and theta0Indicating the far field divergence angle;
the fluctuating intensity transmission of a single photon pulse can be expressed as:
Figure BDA0001805671320000031
wherein, A represents the aperture area,
Figure BDA0001805671320000032
is shown as a whole
Figure BDA0001805671320000033
Normalized intensity of the plane.
In a preferred embodiment of the invention, when the transmission distance is 20km and the aperture of the antenna at the receiving end is 50cm, the single photon capture rate at the receiving end reaches 0.7506 at most.
In a preferred embodiment of the present invention, the average number of single photons transmitted by the single-photon transmission terminal is set to NaAfter being transmitted through an atmospheric channel, the average single photon number counted by the receiving terminal is NbThe transmission rate of a single photon signal transmitted from a transmitting terminal to a receiving terminal can be defined as
Figure BDA0001805671320000034
In a preferred embodiment of the present invention, the detection line of the receiving terminal mainly includes a beam splitter BS, a polarization splitter PBSs, a half-wave plate HWP, and four single photon detectors SPDs, and the optical fiber is respectively connected to the beam splitter BS, the polarization splitter PBSs, and the half-wave plate HWP, and then externally connected to the four detectors SPDs to count the single photons.
Through the technical scheme, the invention has the technical effects that:
the invention provides a single photon receiving efficiency model under the condition of different intensity atmospheric turbulence interference, and in addition, a receiving terminal can ensure higher single photon receiving rate by selecting a proper antenna aperture.
Drawings
Fig. 1 is a diagram showing the variation of the single photon capture rate and the transmission distance between the single photon sending terminal and the satellite detecting terminal.
FIG. 2 is a diagram of the variation of the single photon receiving efficiency of the satellite receiving terminal and the equivalent centroid position of the single photon pulse beam.
Figure 3 is a graph of the variation between single photon counting and atmospheric turbulence at a receiving terminal.
Fig. 4 is a graph showing a relationship between a final key generation rate and a transmission distance.
Fig. 5a is a graph of quantum channel utilization versus temperature, and fig. 5b is a graph of quantum channel utilization versus humidity.
Fig. 6a is a curve of quantum channel utilization rate versus wind speed, and fig. 6b is a curve of quantum channel utilization rate versus humidity.
Fig. 7a is a curve of quantum channel utilization rate versus temperature, and fig. 7b is a curve of quantum channel utilization rate versus wind speed.
Detailed Description
To further explain the technical means and effects of the present invention adopted to achieve the intended purpose, the following detailed description of the embodiments, structural features and effects of the present invention will be made with reference to the accompanying drawings and examples.
In the description of the present invention, it is to be understood that the terms "internally disposed," "externally disposed," "vertical," "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," "outer," and the like are used in the orientations and positional relationships indicated in the drawings, which are used for convenience in describing the present invention and for simplicity in description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated, and thus should not be construed as limiting the present invention.
In addition, in the description of the present invention, "a plurality" means two or more unless otherwise specified.
The terms "connected", "connected" and "fixed" are to be construed broadly, e.g., as meaning a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art through specific situations.
The invention discloses an improvement method for the performance of a free space quantum channel, which comprises the following steps:
a sending terminal of a ground station emits single photon pulses, and the single photon pulses firstly pass through the atmosphere and then are transmitted to a satellite receiving terminal; the satellite receiving terminal reflects the obtained single photon pulse signal to a receiving terminal of the ground station, the receiving terminal receives the signal by adopting a single photon detector to obtain energy hv, and the energy hv triggers a counter to work and simultaneously counts single photons; at time intervals t0,t0+T]In the method, the probability p (n) that the receiving terminal counts n single photons can be expressed as
Figure BDA0001805671320000051
Wherein q is the average number of single photons and can be expressed as
Figure BDA0001805671320000052
Here, p represents the single photon reception efficiency of the receiving terminal, T is the interval of optoelectronics, and i (T) refers to the field strength of the receiving terminal, where T0 represents a certain point in time.
Further, the invention proposes a single photon reception efficiency model which can be expressed as a product of a single photon capture rate and an atmospheric turbulence transmittance.
The single photon receiving efficiency can be used for calculating the single photon counting of the receiving terminal and evaluating the final key generation rate. Meanwhile, by the model, the optical coupling and loss between a signal sending end and a signal receiving end can be analyzed. Thus, the model may be defined as
p＝pacq×K, (3)
Wherein p isacqThe single photon capture rate of the aperture of the telescope antenna is shown, and K represents the efficiency of the optical pulse signal to penetrate through the atmospheric turbulence, namely the fluctuation intensity transmittance of the single photon pulse.
The single photon capture rate of the telescope antenna aperture can be expressed as
Figure BDA0001805671320000053
Wherein a represents the antenna aperture of the receiving end telescope, L is the transmission distance between the single photon emission end and the satellite receiving end, and theta0Indicating the far field divergence angle;
the fluctuating intensity transmission of a single photon pulse can be expressed as
Figure BDA0001805671320000061
Wherein, A represents the aperture area,
Figure BDA0001805671320000062
is shown as a whole
Figure BDA0001805671320000063
Normalized intensity of the plane.
For weak turbulence conditions, the light spot does not play a very important role; for strong turbulence, the shape of the beam is distorted by many small spatial balances. Thus, at the aperture plane, the intensity of the elliptical beam
Figure BDA0001805671320000064
Can be expressed as
Figure BDA0001805671320000065
Wherein the content of the first and second substances,
Figure BDA0001805671320000066
the centroid position of the beam is represented, S represents the true, symmetric and positive spot matrix, and det refers to the determinant value for a certain matrix.
Therefore, by substituting the formula (6) into the formula (5), we can obtain the fluctuation intensity transmittance of the single photon pulse. Since the integration result cannot be simulated by estimation in practice, we adopt the techniques mentioned in the literature to obtain an analytical approximation. Here we consider the location of the beam centroid as
Figure BDA0001805671320000067
And (6) replacing.
Thus, the fluctuating intensity transmittance of a single photon pulse can be expressed as
Figure BDA0001805671320000068
Wherein, K0The transmission is shown at the beam centroid position, and R (epsilon) and lambda (epsilon) are the shape and scale functions, respectively.
Figure BDA0001805671320000071
Figure BDA0001805671320000072
Figure BDA0001805671320000073
Figure BDA0001805671320000074
Wherein, W i 21,2, which are square forms of the semi-axis of the ellipse, the semi-axis W of the ellipse1Has an angle phi epsilon [0, pi/2 ] with the x-axis, and
Figure BDA0001805671320000075
d (ε) represents the Lembert W function, IiAnd (epsilon) represents a bezier function of the i-th order (i ═ 1,2) correction.
Therefore, the single photon reception efficiency expressed by the formula (3) can be rewritten as
Figure BDA0001805671320000076
FIG. 1 depicts the variation of single photon capture rate and transmission distance between a single photon emitting terminal and a satellite detecting terminal, as described in FIG. 1, where θ0The aperture a of the antenna at the receiving end is 5cm,20cm and 50cm respectively at 30 μ rad. With the increase of the transmission distance, the single photon capture rate is reduced sharply, and the single photon capture rate can be improved by increasing the antenna aperture of the receiving end telescope. However, this method makes the implementation of the receiving end very difficult and expensive. Therefore, we must select a proper aperture of the telescope antenna to ensure the normal and effective operation of quantum communication.
From fig. 1, it can be seen that, under the same transmission distance requirement, when the turbulence is strong, the communication cannot be performed because the capture rate of the single photon detector is low. Therefore, when the transmission distance is 20km and the aperture of the receiving end antenna is 50cm, the single photon capture rate of the receiving end can reach 0.7506.
As shown in fig. 2, fig. 2 illustrates the variation of the single photon receiving efficiency of the satellite receiving terminal and the equivalent centroid position of the single photon pulse beam, and it is assumed herein that the single photon capturing rate of the receiving terminal can reach 80%. The weak turbulence condition indicated by (a) in the figure; (b) the indicated weak to medium intensity turbulence conditions; (c) a strongly turbulent flow situation is represented.
As the intensity of the atmospheric turbulence increases, the beam will be continuously broadened and deformed, in other words, the semi-axis of the ellipse will be continuously widened. It is due to such severe beam deformation that the single-photon reception efficiency is continuously decreased. When the semi-axis of the ellipse satisfies the condition W1 2＝W2 2＝W2When (the semi-axis of the ellipse usually has two values, one is the major axis and the minor axis, which is to say when the major and minor axes are equal and equal to w, which is to say when it is circular), equation (9) can be abbreviated
Figure BDA0001805671320000081
I.e. to reach the maximum transmission of the central beam of the single-photon pulse.
Constructing and analyzing a single photon counting model:
the invention adopts a log-normal model to analyze the photon number statistics of a receiving terminal in the log-normal model, and the transmittance intensity of a single photon signal can be expressed as
Figure BDA0001805671320000082
We can estimate the average transmission intensity of a single photon as
Figure BDA0001805671320000091
Wherein the mean of the root mean square radii is
Figure BDA0001805671320000092
W0The spot radius is shown, omega the fresnel constant of the aperture of the receiving terminal,
Figure BDA0001805671320000093
is the intensity of atmospheric turbulence.
In the foregoing, we propose a model of single photon reception efficiency, i.e., p ═ pacqK. The average photon number can be expressed as
Figure BDA0001805671320000094
When the average photon number q is fixed, equation (1) represents the probability that the receiving end detects n photons within the transmission interval T. In practice, however, atmospheric turbulence will cause the average photons to fluctuate, and if the count interval T is much smaller than the turbulence timescale, equation (1) can be replaced by a Mandel equation
Figure BDA0001805671320000095
In the transmission process of single photon signals in a free space quantum channel, due to the influence of atmospheric turbulence, the average photon number q should be subjected to a log-normal probability distribution model in a receiving end counting interval T
Figure BDA0001805671320000096
In the formula (I), the compound is shown in the specification,<q>is the average number of photons measured by the receiving end over the statistical time interval T. In this context we assume that in the case of weak turbulence we are
Figure BDA0001805671320000097
Under the condition of medium-strong turbulence, the flow velocity is
Figure BDA0001805671320000098
The intensity of atmospheric turbulence can be defined as
Figure BDA0001805671320000099
In the formula (I), the compound is shown in the specification,
Figure BDA00018056713200000910
the atmospheric refractive index structure constant is shown, k represents the number of optical pulses, k is 2 pi/lambda ', lambda' is the wavelength of a single photon pulse, and h represents the effective thickness of the atmosphere.
As shown in fig. 3, fig. 3 illustrates the variation between the single photon counting of the receiving terminal and the atmospheric turbulence, and we can arbitrarily select the average value of the single photon counting of the emitting terminal as n-60, the intensity of the atmospheric turbulence
Figure BDA0001805671320000101
Figure BDA0001805671320000101
0,0.5,1.5 and 3.5 are selected, respectively. When no atmospheric fluctuation exists in the atmospheric environment, the peak value of the single photon counting distribution probability function appears at n-60, which indicates that the number of single photons counted by the receiving end is 60, and the receiving end is not influenced by the external atmospheric environment, which is an ideal situation.
When intensity of atmospheric turbulence
Figure BDA0001805671320000102
The method is characterized by a weak turbulence condition, wherein the peak value of the probability function of the single photon counting distribution appears at n-40, which indicates that the atmospheric turbulence has interference on single photon transmission.
When intensity of atmospheric turbulence
Figure BDA0001805671320000103
When the single-photon counting distribution probability function is expressed in a medium-intensity turbulence condition, the peak value of the single-photon counting distribution probability function is shown as n-17, which indicates that the atmospheric turbulence has a large influence on single-photon transmission.
When intensity of atmospheric turbulence
Figure BDA0001805671320000104
The method is characterized by a strong turbulence condition, wherein the peak value of the probability function of the single photon counting distribution appears at n-3, which indicates that the atmospheric turbulence has serious interference on the single photon transmission. For a worse atmosphere environment, namely ultra-strong atmospheric turbulence, the single photon counted by the receiving end at the momentThe number is approximately 0, indicating that single photon pulses cannot be transmitted normally and efficiently in free space quantum channels.
Final key generation rate model analysis:
in the process of transmitting single photons in free space, the average number of photons sent by a single photon emission end (Alice) is assumed to be NaAfter transmission through the atmospheric channel, the average number of photons counted by the receiving end (Bob) is Nb. Therefore, the transmission rate of a single photon signal transmitted from a transmitting end to a receiving end can be defined as
Figure BDA0001805671320000105
From fig. 3, we can observe that the average photon number sent by the transmitting end is 60, and under the interference of the weak turbulence condition, the number of single photons counted by the receiving end is 40; under the interference of medium-intensity turbulence conditions, the number of single photons counted by a receiving end is 17; under the interference of a strong turbulence condition, the number of single photons counted by the receiving end is 3. We can calculate the transmission rate of single photon signals to the receiving end in the weak turbulence channel to be 66.7%; in the medium turbulence channel, the transmission rate of the single photon signal to the receiving end is 28.3%, and in the high turbulence channel, the transmission rate of the single photon signal to the receiving end is about 5%. Therefore, for particularly severe weather conditions, namely the intensity of atmospheric turbulence is very high, the transmission rate of the single photon signal reaching the receiving end is approximately 0, which is not favorable for normal quantum communication.
In the free space quantum channel, the final key generation rate is a very important index for measuring the performance of two-party communication. Here we adopt a BB84 quantum key distribution protocol [30 ] based on no common reference frame]The transmission rate of a single photon emitted by a transmitting end (Alice) is η ═f·η·ηdIn the formula etafIs expressed in terms of atmospheric transmission rate, and etafExp (- β L). Beta represents the atmospheric attenuation coefficient (db/km), etadThe detection efficiency of a receiver (Bob) single photon detector is shown.
In the protocol, the detection circuit of the receiving terminal (Bob) mainly comprises a Beam Splitter (BS) which is mainly used for randomly selecting a measurement basis, a Polarization Beam Splitter (PBSs), a half-wave plate (HWP), four photon detectors (SPDs) and the like. As mentioned previously, η' represents the transmission rate of a single photon emitted by the transmitting end (Alice), Y0Representing the dark count rate of a single photon detector.
Therefore, the temperature of the molten metal is controlled,
Figure BDA0001805671320000111
indicating that the single photons were detected by this detector and not by the other three detectors. If the single photon does not reach the detector at the receiving end, but the single photon counts at the detector end, this situation can be expressed as
Figure BDA0001805671320000112
Finally, the count rate of the single photon pulses at the receiver end can be expressed as dark counts at the receiver end
R0＝η′(1-Y0 3)+4(1-η′)Y0(1-Y0 3)
＝(η′+4(1-η′)Y0)(1-Y0 3) (17)
The receiving end screens the single photon signals, and the counting rate of the single photon pulses after screening can be expressed as
Figure BDA0001805671320000121
In the formula, psWhich refers to the percentage of total qubits that are used to negotiate a key after screening, in the BB84 quantum key distribution protocol,
Figure BDA0001805671320000122
in the process of calculating the QBER (QBER), only the influence caused by the dark count of the detector needs to be considered. The percentage of quantum bit errors caused by dark counts is 50%. Thus, the quantum bit error rate can be expressed as
Figure BDA0001805671320000123
The final key generation rate [36] can be expressed as
Rnet＝Rsift(IAB-IAE) (20)
In the formula IABIndicating mutual information between the sender (Alice) and the receiver (Bob), and IAB＝1-H2(E0)，H2(E0)＝-E0log2(E0)-(1-E0)log2(1-E0)。IAEIndicating mutual information between the sender (Alice) and the eavesdropper (Eve), and IAE≈H2(E0). Thus, in a QKD transport protocol, the final key generation rate can be expressed as
Figure BDA0001805671320000124
In a free space quantum communication system, an atmospheric attenuation coefficient beta is 0.2, and a dark counting rate of a single photon detector is 10-5The detection efficiency of the single photon detector at the receiving end is 90 percent, and the atmospheric turbulence intensity
Figure BDA0001805671320000125
0.5,1.5, 3.5 and 10 are respectively selected to represent weak turbulence, medium intensity turbulence, strong turbulence and super strong turbulence. The final key generation rate versus transmission distance between the two communicating parties under conditions of different intensity turbulence can be described by means of fig. 4.
From fig. 4 we can observe that the transmission distance between two communicating parties is continuously shortened as the intensity of the atmospheric turbulence is increased. Under given conditions, the transmission distance of the single-photon signal in free space under the condition of weak turbulence can reach 41km, and the single-photon signal in free space under the condition of medium-intensity turbulence can reach 41kmThe signal transmission distance can reach 37km, the free space single photon signal transmission distance can reach 28km under the condition of strong turbulence, and the free space single photon signal transmission distance is only about 4km under the condition of superstrong turbulence. Under the condition of strong turbulence, the final key generation rate of single photon pulses in the free space quantum communication system is reduced by about 14 times compared with the condition of weak turbulence; under the condition of super-strong turbulence, the final key generation rate of transmitting message sequences in the free space quantum communication system is only 3.75 x 10-6. Therefore, we can know that the ultra-strong turbulence has very serious interference to the transmission of the free-space single-photon signal.
Constructing a quantum channel link utilization rate model:
assuming that the length of each data frame is fixed, its transmission time is td(seconds). Furthermore, the positive response time interval and the negative corresponding time interval are both tqThe transmission time delay interval of the physical communication link is tp. In this case, the transmission period of each data frame may be represented as td+tp+tq+tp. Now, given an arbitrary data frame at random, it must be retransmitted several times to ensure successful transmission of the data frame, and N is taken to represent the total average number of transmissions of the data frame (the initial transmission state for the first time, and the remaining N-1 is the repeat transmission state). Therefore, we can get the data frame that needs to be transmitted N times to ensure the success of its communication. In this way we can obtain the maximum average link utilization of the physical link (i.e. the average link utilization when the maximum load that can be achieved is transmitted in the physical link) [37 ]]Is composed of
Figure BDA0001805671320000131
Wherein p' represents the error probability of an information bit, and
Figure BDA0001805671320000132
in free space quantum communication systems, the interference of atmospheric turbulence on single photon signal transmission is very severe. In this context, we mainly consider the influence of three factors, namely humidity, temperature and wind speed in the atmospheric environment, on the quantum channel link utilization. Thus, quantum channel link utilization can be defined as
Figure BDA0001805671320000141
In the formula umaxRepresents the maximum value of the humidity range in the atmosphere, TmaxDenotes the maximum value of the temperature range in the atmosphere, vmaxRepresenting the maximum value of the wind speed in the atmosphere.
Therefore, we can deduce the quantum channel link utilization under the condition of atmospheric turbulence as
Figure BDA0001805671320000142
In the case of weak, moderate and strong turbulence, the transmission rates of the single photon signals to the receiver detector are 66.7%, 28.3% and 5%, respectively. In this context, the information error rate p' is 0.06, and under the condition of different intensities of turbulence, the maximum link utilization of the quantum channel varies with the atmospheric environmental factors as shown in fig. 5,6 and 7.
Assuming that the wind speed of a single photon in the free space quantum channel transmission process is 4m/s, as shown in fig. 5a and 5b, the maximum link utilization under the weak turbulence condition is 0.4478; from fig. 5b it is observed that the maximum link utilization is 0.19 in case of medium intensity turbulence; in case of strong turbulence, the variation trend of the maximum link utilization of the quantum channel is similar to that of medium intensity turbulence. Therefore, the maximum link utilization in case of strong turbulence is 0.033.
Simulation results show that the link utilization rate of the quantum channel has more obvious trend along with the change of the temperature, namely the temperature is relatively higher than the humidity, and the influence on the maximum link utilization rate of the quantum channel is larger.
As shown in fig. 6a, fig. 6b, assuming that the temperature of a single photon during free space quantum channel transmission is 15 ℃, it can be observed from fig. 6(a) that the maximum link utilization rate is 0.418 in the case of weak turbulence; it is observed from fig. 6(b) that the maximum link utilization is 0.177 in the case of medium intensity turbulence; in case of strong turbulence, the variation trend of the maximum link utilization of the quantum channel is similar to that of medium intensity turbulence. Thus, the maximum link utilization in a strong turbulent situation is 0.031.
Simulation results show that the link utilization rate of the quantum channel changes more obviously along with the wind speed, namely the wind speed relative to the humidity has a larger influence on the maximum link utilization rate of the quantum channel.
Assuming a single photon humidity of 0.5 during free-space quantum channel transmission as shown in fig. 7a and 7b, the maximum link utilization of 0.5225 in the case of weak turbulence can be observed from fig. 7 (a); it is observed from fig. 6(b) that the maximum link utilization is 0.2217 in the case of medium intensity turbulence; in case of strong turbulence, the variation trend of the maximum link utilization of the quantum channel is similar to that of medium intensity turbulence. Thus, the maximum link utilization in case of strong turbulence is 0.039. Simulation results show that the link utilization rate of the quantum channel has more obvious trend along with the change of the temperature, namely the temperature has larger influence on the maximum link utilization rate of the quantum channel relative to the wind speed.
Through the analysis, the molecular irregular motion in the atmospheric environment is enhanced along with the increase of the temperature in the free space quantum communication system; the absorption and scattering of photons by water molecules in the external environment are enhanced with the increase of relative humidity; the irregular movement of particles in the atmospheric environment is also enhanced along with the increase of the wind speed, which has great influence on the link utilization rate of the quantum channel, and is particularly remarkable under the condition of strong turbulence. Meanwhile, as can be seen from simulation analysis, the temperature may be the most important interference factor among the above-mentioned influencing factors.
In summary, in the transmission process of quantum light in a free space channel, based on an approximate elliptical beam model, we propose a single photon receiving efficiency model under different intensity atmospheric turbulence interference conditions. The result shows that the receiving terminal can ensure higher single photon receiving rate by selecting proper antenna aperture. In this case, the text analyzes and calculates the average photon number and the final key generation rate under different intensity atmospheric turbulence interferences, and analyzes the influence of atmospheric parameters on the quantum channel utilization rate. The results indicate that temperature may be the most important of the influencing factors.
Under the interference of weak turbulence, medium intensity turbulence and strong turbulence, simulation results show that when the atmospheric temperature is 15 ℃, the wind speed is 5m/s, the relative humidity is 0.5, and the quantum channel link utilization rates are 0.31,0.13 and 0.023 respectively. As the intensity of the atmospheric turbulence increases, the phenomena of beam drift, broadening and distortion become more and more significant. In other words, this causes the elliptical half-axes to continuously broaden, while reducing single photon reception efficiency, key generation rate, and quantum channel utilization. Especially under the condition of strong turbulence, single photon counting is not ideal, the key generation rate is low, and the quantum channel utilization rate is only 0.03. Therefore, under extremely harsh atmospheric conditions, we should avoid normal single photon transport.
According to the atmospheric parameters, the parameters of the communication system can be reasonably adjusted, and further the influence of atmospheric turbulence on the single photon transmission performance is reduced. Under the interference of atmospheric turbulence with different intensities, single photon transmission in an atmospheric channel is calculated and simulated, and a foundation is laid for the research of turbulent quantum communication.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (6)

1. A method for improving the performance of a free-space quantum channel, comprising the steps of:
a sending terminal of a ground station emits single photon pulses, and the single photon pulses firstly pass through the atmosphere and then are transmitted to a satellite receiving terminal;
the satellite receiving terminal reflects the obtained single photon pulse to a receiving terminal of the ground station, the receiving terminal receives signals by adopting a single photon detector to obtain energy hv, and the energy hv triggers a counter to work and simultaneously counts single photons;
at time intervals t0,t0+T]In the method, the probability p (n) that the receiving terminal counts n single photons can be expressed as
Figure FDA0002993512020000011
Wherein q is the average number of single photons and can be expressed as
Figure FDA0002993512020000012
Here, p represents the single photon reception efficiency of the receiving terminal, T is the interval of optoelectronics, and i (T) refers to the field strength of the receiving terminal, where T0 represents a certain point in time.
2. The method of claim 1 for improving free-space quantum channel performance, wherein the receive terminal single photon reception efficiency p is defined as:
p＝pacq×K (3)
wherein p isacqThe single photon capture rate of the aperture of the telescope antenna is shown, and K represents the efficiency of the optical pulse signal to penetrate through the atmospheric turbulence, namely the fluctuation intensity transmittance of the single photon pulse.
3. The method of claim 2 for improved free-space quantum channel performance, wherein the single photon capture rate of the telescope antenna aperture can be expressed as:
Figure FDA0002993512020000013
in the formula, a tableThe antenna aperture of the receiving end telescope is shown, L is the transmission distance between the single photon emission end and the satellite receiving end, theta0Indicating the far field divergence angle;
the fluctuating intensity transmission of a single photon pulse can be expressed as:
Figure FDA0002993512020000021
wherein, A represents the aperture area,
Figure FDA0002993512020000022
is shown as a whole
Figure FDA0002993512020000023
Normalized intensity of the plane.
4. The improvement method for the performance of the free-space quantum channel as claimed in claim 2, wherein the single photon capture rate of the receiving end reaches 0.7506 maximum when the transmission distance is 20km and the aperture of the receiving end antenna is 50 cm.
5. The method of claim 1 for improving free-space quantum channel performance, wherein the average number of single photons transmitted by a single photon transmission terminal is set to be NaAfter being transmitted through an atmospheric channel, the average single photon number counted by the receiving terminal is NbThe transmission rate of a single photon signal transmitted from a transmitting terminal to a receiving terminal can be defined as
Figure FDA0002993512020000024
6. The method as claimed in claim 2, wherein the detection circuit of the receiving terminal mainly includes a beam splitter BS, a polarization splitter PBSs, a half-wave plate HWP and four single photon detectors SPDs, and the optical fiber is respectively connected to the beam splitter BS, the polarization splitter PBSs and the half-wave plate HWP, and then externally connected to the four single photon detectors SPDs to count the single photons.
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