CN110492991B - Parameter estimation method and system based on free space CVQKD system - Google Patents

Parameter estimation method and system based on free space CVQKD system Download PDF

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CN110492991B
CN110492991B CN201910314197.9A CN201910314197A CN110492991B CN 110492991 B CN110492991 B CN 110492991B CN 201910314197 A CN201910314197 A CN 201910314197A CN 110492991 B CN110492991 B CN 110492991B
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黄鹏
柴庚
汪超
曾贵华
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Shanghai Circulation Quantum Technology Co ltd
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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
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Abstract

The invention provides a parameter estimation method and a system based on a free space CVQKD system, which are used for dividing sub-channels of an atmospheric channel, dividing the atmospheric channel into a plurality of sub-channels through a flicker index of local oscillator light intensity of a receiving end, and simultaneously obtaining shot noise of the sub-channels; estimating system related parameters, obtaining estimated values of related parameters under different sub-channels through parameter estimation according to the divided sub-channels, and then calculating a key rate according to the parameter estimated values so as to judge whether the channel is safe or not; and (4) extracting the key, reserving the sub-channel which has larger contribution to the key rate through a post-selection method, and extracting the key from the sub-channel to obtain the final key of the system. The method and the device perform sub-channel division on the atmospheric channel of the free space CVQKD system to obtain the parameter estimation value and the real-time key rate under each sub-channel, and improve the system performance by combining the post-selection technology.

Description

Parameter estimation method and system based on free space CVQKD system
Technical Field
The invention relates to the technical field of information security, in particular to a parameter estimation method and a parameter estimation system based on a free space CVQKD system, in particular to a parameter estimation method for continuous variable quantum key distribution, which is designed based on free space Gaussian modulation coherent state continuous variable quantum key distribution (GMCS CVQKD).
Background
Continuous variable quantum key distribution is a technology different from traditional communication, and the unconditional safety of communication is realized mainly by using an uncertainty principle and a quantum state unclonable theorem. The optical fiber channel CVQKD has attracted many researchers to participate in research because of its potential advantages compatible with existing optical communication technologies. In order to make the free space CVQKD and the optical fiber channel CVQKD better merge and develop, research on continuous variable quantum key distribution under the free space channel has become one of the research hotspots of the CVQKD in recent years.
CVQKD generally includes two phases: (1) quantum information transmission stage: the quantum signal is transmitted through a quantum channel and then measured by a zero/heterodyne detector; (2) classical information post-processing stage: part of the data is evaluated for system security by applying parameter estimation, and the rest part extracts a final key by technologies such as reverse negotiation, privacy enhancement and the like. And the parameter estimation is used as a key loop in the post-processing stage of the CVQKD classical information, which helps the communication parties to evaluate the actual safety of the system and obtain parameters relevant for subsequent processing. In the case where the quantum channel is estimated by a legitimate correspondent, the principles of quantum mechanics impose an upper bound on the information that may be revealed to a potential eavesdropper. However, the study of free-space channel CVQKD parameter estimation methods is currently almost blank. The transmittance of the free-space channel fluctuates randomly in time compared to the optical fiber channel, and therefore, the parameter estimation method of the optical fiber channel CVQKD cannot be directly applied to the free-space channel CVQKD.
The prior art related to the present application is patent document CN104539582A, which discloses a continuous variable quantum key distribution security defense method, including: step A: shot noise monitoring, namely evaluating shot noise variance by monitoring local oscillator light intensity of a receiving end in real time; and B: calculating a key rate, namely calculating an operation key rate according to the real-time shot noise variance estimated in the step A; the two steps are executed simultaneously and in parallel. The method is used for monitoring the local oscillation light at the receiving end of the CVQKD system, acquiring the shot noise variance during the operation of the system, and acquiring the real-time operation key rate of the system by combining a parameter estimation method so as to provide safety early warning for the safety of the system. However, the above patent document is designed for a constant transmittance, and is applied only to an optical fiber channel.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a parameter estimation method and system based on a free space CVQKD system.
The invention provides a parameter estimation system based on a free space CVQKD system, which comprises:
a sub-channel division module: the receiving end separates the optical signal sent by the sending end to obtain signal light and local oscillator light, and divides an atmospheric channel into a plurality of sub-channels through the flicker index of the local oscillator light to obtain shot noise of each sub-channel;
a parameter estimation module: the receiving end detects the signal light to obtain initial correlation information, parameter evaluation is carried out on each sub-channel based on the initial correlation information to obtain a parameter estimation value, and a key rate is calculated by combining the parameter estimation value and shot noise;
a key selection module: and extracting the key rate, and selecting the key rate of each sub-channel to obtain a final key.
The invention provides a parameter estimation method based on a free space CVQKD system, which comprises the following steps:
a sub-channel dividing step: the receiving end separates the optical signal sent by the sending end to obtain signal light and local oscillator light, and divides an atmospheric channel into a plurality of sub-channels through the flicker index of the local oscillator light to obtain shot noise of each sub-channel;
a parameter estimation step: the receiving end detects the signal light to obtain initial correlation information, parameter evaluation is carried out on each sub-channel based on the initial correlation information to obtain a parameter estimation value, and a key rate is calculated by combining the parameter estimation value and shot noise;
and a key selection step: and extracting the key rate, and selecting the key rate of each sub-channel to obtain a final key.
Preferably, the transmitting end modulates the coherent state signal by using a gaussian random number to form a modulated quantum signal, and transmits the quantum signal to the receiving end through an atmospheric channel;
the receiving end divides the local oscillator light through the beam splitter, divides the atmospheric channel into M sub-channels according to the flicker index monitoring of the light intensity of the local oscillator light, obtains the shot noise of each sub-channel, and records as { N }k}k＝1,2,…,MWhere k denotes the kth sub-channel, NkRepresents the shot noise of the kth sub-channel and M represents the total number of sub-channels.
Preferably, the flicker index is a ratio of a light intensity fluctuation variance of the local oscillator light to a light intensity mean square, and is calculated by the following formula:
Figure BDA0002032543110000031
wherein the content of the first and second substances,
Figure BDA0002032543110000032
a flicker index representing the intensity of the local oscillator light;
r represents a deviation value of the centroid of the received beam from the center of the receive aperture;
l represents a transmission distance;
I2(r, L) represents instantaneous local oscillator light intensity under real-time monitoring;
i (r, L) represents the instantaneous local oscillator light intensity under real-time monitoring;
u represents a voltage signal corresponding to the instantaneous light intensity after photoelectric conversion;
<. > indicates that statistical averages were made.
Preferably, the sending end sends the shared data { x to the receiving endi}i＝1,2,…,NAfter the receiving end receives the shared data after detecting, extracting the storage data { y of each sub-channeli}i＝1,2,…,NObtaining parameter estimation data
Figure BDA0002032543110000033
The following relationships are satisfied:
Figure BDA0002032543110000034
wherein, tkRepresenting the correlation coefficient of the sending end data and the receiving end data on the k-th sub-channel;
xkrepresents the sender data on the k-th sub-channel;
ykrepresents the receiving end data on the k-th sub-channel;
zkrepresenting the k sub-channelNoise above, mean is zero, variance
Figure BDA0002032543110000035
(ii) a gaussian distribution;
eta represents the detection efficiency obtained by the pre-selection measurement of the receiving end;
velrepresenting electrical noise resulting from a preselected measurement at the receiving end;
Tkrepresents the transmittance of the k-th sub-channel;
εkrepresents the over-noise of the k-th sub-channel;
Nkis the shot noise of the k-th sub-channel.
Preferably, the estimate of the parameter is obtained by:
Figure BDA0002032543110000036
wherein the content of the first and second substances,
Figure BDA0002032543110000037
an estimated value representing a correlation coefficient between the transmitter data and the receiver data on the kth sub-channel;
Figure BDA0002032543110000038
represented on the k-th sub-channel in M groups of data
Figure BDA0002032543110000039
Randomly selected m groups of data for parameter evaluation;
Figure BDA0002032543110000041
representing the noise z on the k-th sub-channelkAn estimate of the variance of (c);
Figure BDA0002032543110000042
representing the k-th intra-subchannel signalAnd (4) modulating the variance estimation value.
Preferably, the estimated value of the parameter of the kth sub-channel is obtained by the following formula:
Figure BDA0002032543110000043
wherein the content of the first and second substances,
Figure BDA0002032543110000044
an estimate value representing a signal modulation variance in the kth subchannel;
Figure BDA0002032543110000045
an estimated value representing the channel transmittance of the kth sub-channel;
Figure BDA0002032543110000046
representing an estimate of the over-noise of the k-th sub-channel,
Figure BDA0002032543110000047
representing an estimate of the total noise of the k-th sub-channel.
Preferably, the estimated value of the parameter of the atmospheric channel is obtained by the following formula:
Figure BDA0002032543110000048
wherein the content of the first and second substances,
Figure BDA0002032543110000049
represents the average transmittance of the atmospheric channel;
m' represents the channel transmittance distribution number of the atmospheric subchannel;
Figure BDA00020325431100000410
indicates the channel transmittance TkA corresponding probability;
Figure BDA00020325431100000411
represents the over-noise epsilonkA corresponding probability;
Figure BDA00020325431100000412
representing total noise
Figure BDA00020325431100000413
A corresponding probability;
Figure BDA00020325431100000414
representing modulation variance
Figure BDA00020325431100000415
A corresponding probability;
Figure BDA00020325431100000416
representing the average over-noise of the atmospheric channel;
Figure BDA00020325431100000417
is the signal mean modulation variance;
Figure BDA00020325431100000418
is the total noise of the atmospheric channel;
Figure BDA00020325431100000419
is the total noise of the kth subchannel.
Preferably, the K sub-channel key rate K(k)And the system key rate K is calculated as follows:
Figure BDA00020325431100000420
K＝(1-P)(βIAB-χBE) (6b)
wherein, K(k)Represents the k-th sub-channel key rate;
β represents the reverse negotiation efficiency;
Figure BDA0002032543110000051
representing the mutual information quantity between the sending end and the receiving end on the kth sub-channel;
Figure BDA0002032543110000052
representing the mutual information quantity between the eavesdropper and the receiving end on the kth sub-channel;
k represents the system key rate;
IABrepresenting the mutual information quantity between a sending end and a receiving end in the system;
χBErepresenting the mutual information quantity between an eavesdropper and a receiving end in the system; pkRepresenting a communication outage probability for the kth sub-channel;
p represents the system communication outage probability.
Preferably, the first and second electrodes are formed of a metal,
Figure BDA0002032543110000053
Figure BDA0002032543110000054
Figure BDA0002032543110000055
Figure BDA0002032543110000056
wherein the content of the first and second substances,
g (x) denotes Shannon entropy, G (x) ═ x +1 log2(x+1)-xlog2x；
Figure BDA0002032543110000057
A sine eigenvalue representing the covariance matrix on the kth subchannel;
λithe sincerous eigenvalues of the system covariance matrix are represented;
in particular, the amount of the solvent to be used,
in the k-th sub-channel,
Figure BDA0002032543110000058
wherein "+" in the formula (9-a) means
Figure BDA0002032543110000059
The value of (A), "-" indicates
Figure BDA00020325431100000510
A value of (d);
Figure BDA00020325431100000511
Figure BDA00020325431100000512
wherein the content of the first and second substances,
Figure BDA00020325431100000513
Figure BDA00020325431100000514
represents the linear noise of the k-th sub-channel,
Figure BDA00020325431100000515
Ak、Bk、CK、DKare respectively used as a reference for simplifying formula operation in the k-th sub-channel, and have no specific
Refers to a meaning;
χhrepresenting receiver probe noise,. chih＝[(1-η)+vel]/η
Figure BDA0002032543110000061
In the case of an atmospheric air channel,
Figure BDA0002032543110000062
wherein the content of the first and second substances,
Figure BDA0002032543110000063
Figure BDA0002032543110000064
Figure BDA0002032543110000065
wherein "+" in the formula (10-c) means λ3The value of (A) (-) represents λ4A value of (d);
Figure BDA0002032543110000066
Figure BDA0002032543110000067
which represents the linear noise of the atmospheric channel,
Figure BDA0002032543110000068
χhrepresenting receiver probe noise,. chih＝[(1-η)+vel]/η；
A. B, C, D are respectively used as the index for simplifying formula operation in the atmosphere channel, and have no specific reference meaning;
Figure BDA0002032543110000069
the key rate of each sub-channel can be obtained by calculating the formula (6-a) according to the formulas (7-a), (8-a) and (9-a) - (9-d), and the average key rate of the atmospheric channel can be obtained by calculating the formula (6-b) according to the formulas (7-b), (8-b) and (10-a) - (10-d).
Preferably, the detection of the signal light by the receiving end is accomplished by a detector, wherein the detector is a calibrated Homodyne detector; the estimates of the parameter estimates include channel transmittance, channel over-noise, modulation variance, and channel total noise.
Compared with the prior art, the invention has the following beneficial effects:
1. the method is based on the channel characteristics of the atmospheric channel and continuous variable quantum key distribution, obtains the shot noise of the sub-channel by dividing the sub-channel, carries out parameter estimation, and can accurately judge whether the system running state is safe, so that a receiving end selects to extract the key after carrying out the sub-channel;
2. the method for processing the received data at the receiving end is simple and efficient to realize and has good application prospect in a free space CVQKD system.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic reference diagram of a free space CVQKD system;
FIG. 2 is a flow chart of the present invention.
The figures show that: and Alice: a sending end; and Bob: a receiving end; src: a light source; RNG: a random number generator; mod: modulator(ii) a PC: a polarization controller; BS: a beam splitter; HD: a Homodyne detector; t: a channel transmittance; p: probability corresponding to channel transmittance; t isi: channel transmittance of the ith subchannel;
Figure BDA0002032543110000071
probability corresponding to the ith sub-channel transmittance; epsilon: excessive noise; eta: detecting efficiency of a detector at a receiving end; v: receiving end noise variance; xA，PA: a Gaussian random number sequence; delta XA: canonical position before modulation; delta PA: positive moment before modulation; x: canonical position after modulation; p: regular momentum after modulation; x (p): receiving a measurement of the regular position (momentum) of the end; g, F0: and the receiving end assists the quantum state detected by the Homodyne.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
The invention provides a parameter estimation method based on a free space CVQKD system, which comprises the following steps:
a sub-channel dividing step: the receiving end separates the optical signal sent by the sending end to obtain signal light and local oscillator light, and divides an atmospheric channel into a plurality of sub-channels through the flicker index of the local oscillator light to obtain shot noise of each sub-channel;
a parameter estimation step: the receiving end detects the signal light to obtain initial correlation information, parameter evaluation is carried out on each sub-channel based on the initial correlation information to obtain a parameter estimation value, and a key rate is calculated by combining the parameter estimation value and shot noise;
and a key selection step: and extracting the key rate, and selecting the key rate of each sub-channel to obtain a final key.
Specifically, the transmitting end modulates coherent state signals by using Gaussian random numbers to form modulated quantum signals, and transmits the quantum signals to the receiving end through an atmospheric channel;
the receiving end divides the local oscillator light through the beam splitter, divides the atmospheric channel into M sub-channels according to the flicker index monitoring of the light intensity of the local oscillator light, obtains the shot noise of each sub-channel, and records as { N }k}k＝1,2,…,MWhere k denotes the kth sub-channel, NkRepresents the shot noise of the kth sub-channel and M represents the total number of sub-channels.
Specifically, the flicker index is a ratio of a light intensity fluctuation variance of the local oscillation light to a light intensity mean square, and is calculated by the following formula:
Figure BDA0002032543110000081
wherein the content of the first and second substances,
Figure BDA0002032543110000082
a flicker index representing the intensity of the local oscillator light;
r represents a deviation value of the centroid of the received beam from the center of the receive aperture;
l represents a transmission distance;
i (r, L) represents the instantaneous local oscillator light intensity under real-time monitoring; i is2(r, L) represents the square of the instantaneous local oscillator light intensity under real-time monitoring;
u represents a voltage signal corresponding to the instantaneous light intensity after photoelectric conversion;
<. > indicates that statistical averages were made.
Specifically, the sending end sends shared data { x to the receiving endi}i＝1,2,…,NAfter the receiving end receives the shared data after detecting, extracting the storage data { y of each sub-channeli}i＝1,2,…,NObtaining parameter estimation data
Figure BDA0002032543110000083
The following relationships are satisfied:
Figure BDA0002032543110000084
wherein, tkRepresenting the correlation coefficient of the sending end data and the receiving end data on the k-th sub-channel;
xkrepresents the sender data on the k-th sub-channel;
ykrepresents the receiving end data on the k-th sub-channel;
zkrepresenting noise on the k-th sub-channel, satisfying a mean of zero, variance
Figure BDA0002032543110000085
(ii) a gaussian distribution;
eta represents the detection efficiency obtained by the pre-selection measurement of the receiving end;
velrepresenting electrical noise resulting from a preselected measurement at the receiving end;
Tkrepresents the transmittance of the k-th sub-channel;
εkrepresents the over-noise of the k-th sub-channel;
Nkis the shot noise of the k-th sub-channel.
Specifically, the estimated value of the parameter is obtained by the following formula:
Figure BDA0002032543110000091
wherein the content of the first and second substances,
Figure BDA0002032543110000092
an estimated value representing a correlation coefficient between the transmitter data and the receiver data on the kth sub-channel;
Figure BDA0002032543110000093
represented on the k-th sub-channel in M groups of data
Figure BDA0002032543110000094
Randomly selected m groups of data for parameter evaluation;
Figure BDA0002032543110000095
representing the noise z on the k-th sub-channelkAn estimate of the variance of (c);
Figure BDA0002032543110000096
representing the signal modulation variance estimate in the kth subchannel.
Specifically, the estimated value of the parameter of the kth sub-channel is obtained by the following formula:
Figure BDA0002032543110000097
wherein the content of the first and second substances,
Figure BDA0002032543110000098
an estimate representing a signal modulation variance within the kth subchannel;
Figure BDA0002032543110000099
an estimated value representing the channel transmittance of the kth sub-channel;
Figure BDA00020325431100000910
representing the estimated value of the over-noise of the k-th sub-channel,
Figure BDA00020325431100000911
representing an estimate of the total noise of the k-th sub-channel.
Specifically, the estimated value of the parameter of the atmospheric channel is obtained by the following formula:
Figure BDA00020325431100000912
wherein the content of the first and second substances,
Figure BDA00020325431100000913
represents the average transmittance of the atmospheric channel;
m' represents the channel transmittance distribution number of the atmospheric subchannel;
Figure BDA00020325431100000914
indicates the channel transmittance TkA corresponding probability;
Figure BDA00020325431100000915
represents the over-noise epsilonkA corresponding probability;
Figure BDA00020325431100000916
representing total noise
Figure BDA00020325431100000917
A corresponding probability;
Figure BDA00020325431100000918
representing modulation variance
Figure BDA00020325431100000919
A corresponding probability;
Figure BDA00020325431100000920
representing the average over-noise of the atmospheric channel;
Figure BDA00020325431100000921
is the signal mean modulation variance;
Figure BDA00020325431100000922
is the total noise of the atmospheric channel;
Figure BDA00020325431100000923
is the total noise of the kth subchannel.
In particular, the K-th sub-channel key rate K(k)And the system key rate K is calculated as follows:
Figure BDA0002032543110000101
K＝(1-P)(βIAB-χBE) (6b)
wherein, K(k)Represents the k-th sub-channel key rate;
β represents the reverse negotiation efficiency;
Figure BDA0002032543110000102
representing the mutual information quantity between the sending end and the receiving end on the kth sub-channel;
Figure BDA0002032543110000103
representing the mutual information quantity between the eavesdropper and the receiving end on the kth sub-channel;
k represents the system key rate;
IABrepresenting the mutual information quantity between a sending end and a receiving end in the system;
χBErepresenting the mutual information quantity between an eavesdropper and a receiving end in the system;
Pkrepresenting a communication outage probability for the kth sub-channel;
p represents the system communication outage probability.
Specifically, the detection of the signal light by the receiving end is completed by a detector, wherein the detector is a calibrated Homodyne detector; the estimates of the parameter estimates include channel transmittance, channel over-noise, modulation variance, and channel total noise.
The invention provides a parameter estimation system based on a free space CVQKD system, which comprises:
a sub-channel division module: the receiving end separates the optical signal sent by the sending end to obtain signal light and local oscillator light, and divides an atmospheric channel into a plurality of sub-channels through the flicker index of the local oscillator light to obtain shot noise of each sub-channel;
a parameter estimation module: the receiving end detects the signal light to obtain initial correlation information, parameter evaluation is carried out on each sub-channel based on the initial correlation information to obtain a parameter estimation value, and a key rate is calculated by combining the parameter estimation value and shot noise;
a key selection module: and extracting the key rate, and selecting the key rate of each sub-channel to obtain a final key.
The invention is further elucidated with reference to the following figures.
The invention aims to provide a parameter estimation method based on a free space CVQKD system, which is designed based on a Gaussian modulation coherent state continuous variable quantum key distribution (GMCS CVQKD) system and is designed aiming at random variation of transmittance and excessive noise in a free space channel, wherein the continuous variable quantum key distribution technology becomes an important branch of a communication technology because of the advantages of unconditional safety and the like in physics, and the parameter estimation helps both communication parties to evaluate the actual safety of the system and obtain parameters related to subsequent processing as a key loop in a CVQKD classic information post-processing stage, so that the parameters become a very important part in a system data processing module. The receiving end preprocesses the atmospheric channel, namely sub-channel division of the atmospheric channel; firstly, parameter estimation is carried out on each sub-channel, unsafe sub-channels are abandoned, and then sub-channels which greatly contribute to the key rate are screened out through a post-selection method, so that the final key of the system is obtained.
As shown in fig. 1, the present invention provides a parameter estimation method based on a free space continuous variable quantum key distribution system, which includes the following steps: sub-channel division, parameter estimation and post-selection. The transmitting end (Alice end) transmits the coherent state signal light and the local oscillator light which are subjected to Gaussian modulation to the receiving end (Bob end) through an atmospheric channel by time division multiplexing and polarization multiplexing.
And a sub-channel division stage: the method comprises the steps that a Bob end separates signal light and local oscillation light sent by an Alice end through polarization demultiplexing, then partial local oscillation light is separated through a beam splitter, corresponding voltage signals are obtained through a photoelectric converter, and a flicker index is obtained through a formula (1)
Figure BDA0002032543110000111
According to the flicker index of the local oscillator light intensity to
Figure BDA0002032543110000112
Is centered
Figure BDA0002032543110000113
The range is divided into a sub-channel, and the shot noise of the sub-channel is obtained through a shot noise variance calibration technology.
A parameter estimation stage: the Bob end detects the quantum signal light through a Homodyne detector to obtain initial correlation information, then the Bob end and the Alice end use part of the information to perform parameter evaluation on an atmospheric channel to obtain modulation variance, channel transmittance, noise passing and total noise parameters on each sub-channel, and calculate sub-channel key rate and system key rate by combining shot noise and negotiation efficiency so as to judge the safety of the CVQKD system.
And a post-selection stage: and screening the sub-channels with the key rate higher than the safety threshold value according to the key rate of the sub-channels in the parameter estimation stage to be used as candidate channels for extracting the keys, and then selecting the sub-channels with larger contribution to the keys by combining a post-selection technology to extract a final key.
Through the process, the sub-channel key rate and the system key rate can be obtained through parameter estimation when the CVQKD system runs, on one hand, the system safety can be judged, and on the other hand, the system key rate is improved by combining with a post-selection technology.
Preferably, the above-mentioned phases are performed simultaneously. A sender completes Gaussian modulation on a coherent state through amplitude modulation and phase modulation, and then sends quantum signals and local oscillator light to a receiving end through an atmospheric channel through polarization multiplexing and time division multiplexing; after a receiving end receives quantum signals and local oscillator light sent by a sending end through polarization demultiplexing, a part of local oscillator light is divided through a beam splitter, then corresponding voltage signals are obtained through photoelectric conversion, a corresponding flicker index is obtained through calculation according to a formula (1), meanwhile, corresponding shot noise is obtained through a calibrated Homodyne detector, and then, an atmospheric channel is divided into a plurality of sub-channels through the receiving end according to the flicker index. The data negotiation between the sending end and the receiving end is a reverse negotiation process.
As shown in fig. 2, the present invention is implemented by the following steps:
step 1: the transmitting end modulates coherent state signals by using Gaussian random numbers and transmits the modulated quantum signals to the receiving end through an atmospheric channel; the receiving end divides a part of received local oscillation light through the beam splitter, then divides the atmospheric channel into M sub-channels according to the flicker index monitoring of the local oscillation light intensity, and simultaneously obtains the shot noise value { N ] of each sub-channelk}k＝1,2,…,M；
Step 2: the receiving end completes the detection of the quantum signal through the detector to obtain the key data. After the sending end and the receiving end finish data negotiation, the sending end sends shared data { x to the receiving end through a classical channeli}i＝1,2,…,NAfter receiving the shared data, the receiving end extracts the corresponding data { y stored by the quantum channeli}i＝1,2,…,N；
And step 3: the receiving end transmits the data { (x)i,yi)}i＝1,2,…,NCorresponding to the M sub-channels divided in the step 1 to obtain
Figure BDA0002032543110000121
Then obtaining parameters such as transmittance parameter, modulation variance parameter and noise passing parameter of each sub-channel by parameter estimation method, calculating sub-channel key rate by combining negotiation efficiency, and judging the key rate of the sub-channel at this stageWhether the communication is safe or not;
and 4, step 4: and the receiving end screens out the sub-channels which have larger contribution to the system key rate by a post-selection method in the sub-channel range of which the key rate is higher than the safety threshold value, and extracts the final key from the sub-channels.
The above steps are performed simultaneously.
Preferably, said step 1, in particular:
the sub-channels of the atmospheric channel are divided according to the flicker index of the light intensity of the local oscillator
Figure BDA0002032543110000122
Real-time monitoring of, then
Figure BDA0002032543110000123
Is centered
Figure BDA0002032543110000124
In the range of one sub-channel, the flicker index
Figure BDA0002032543110000125
The calculation is as follows:
Figure BDA0002032543110000126
wherein, I (r, L) represents the instantaneous light intensity, U represents the voltage signal corresponding to the light intensity after photoelectric conversion, L represents the statistical average, and r represents the deviation between the receiving beam and the receiving aperture.
Preferably, said step 3, in particular:
alice end and Bob end exchange m groups of data in each sub-channel
Figure BDA0002032543110000128
For parameter estimation, the following relationship is satisfied under the gaussian model for the kth sub-channel:
yk＝tkxk+zk (2)
wherein the content of the first and second substances,
Figure BDA0002032543110000129
zkmean value of zero and variance
Figure BDA00020325431100001210
Of Gaussian noise, η and velIs the detection efficiency and electrical noise of the Bob terminal, TkIs the transmittance of the kth sub-channel, εkIs the over-noise of the k-th sub-channel, NkIs the shot noise of the k-th sub-channel.
Obtaining the estimated value of the coefficient in the formula (2) according to the maximum likelihood estimation theory,
Figure BDA0002032543110000131
wherein the content of the first and second substances,
Figure BDA0002032543110000132
is the modulation variance estimate for the channel in the kth subchannel.
By the parameter evaluation method, the estimation value of the related parameter of the kth sub-channel is further obtained,
Figure BDA0002032543110000133
therefore, the estimated value of the relevant parameter of the air channel is,
Figure BDA0002032543110000134
wherein the content of the first and second substances,
Figure BDA0002032543110000135
is the average transmission rate of the atmospheric channel,
Figure BDA0002032543110000136
is the average over-noise of the atmospheric channel,
Figure BDA0002032543110000137
is the signal-averaged modulation variance and,
Figure BDA0002032543110000138
is the total noise of the atmospheric channel and,
Figure BDA0002032543110000139
is the total noise of the kth subchannel.
Preferably, said step 3, in particular:
k sub-channel key rate K(k)And the system key rate K is such that,
Figure BDA00020325431100001310
wherein the content of the first and second substances,
Figure BDA00020325431100001311
Figure BDA00020325431100001312
Figure BDA00020325431100001313
Figure BDA00020325431100001314
and the number of the first and second electrodes,
Figure BDA00020325431100001315
Figure BDA00020325431100001316
Figure BDA00020325431100001317
Figure BDA0002032543110000141
Figure BDA0002032543110000142
Figure BDA0002032543110000143
Figure BDA0002032543110000144
Figure BDA0002032543110000145
Figure BDA0002032543110000146
Figure BDA0002032543110000147
Figure BDA0002032543110000148
the key rate of each sub-channel can be obtained by calculation according to the formulas (7-a), (8-a) and (9-a) - (9-d), and the average key rate of the atmospheric channel can be obtained by calculation according to the formulas (7-b), (8-b) and (10-a) - (10-d).
Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and individual modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps into logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (8)

1. A parameter estimation method based on a free space CVQKD system is characterized by comprising the following steps:
a sub-channel dividing step: the receiving end separates the optical signal sent by the sending end to obtain signal light and local oscillator light, and divides an atmospheric channel into a plurality of sub-channels through the flicker index of the local oscillator light to obtain shot noise of each sub-channel;
a parameter estimation step: the receiving end detects the signal light to obtain initial correlation information, parameter evaluation is carried out on each sub-channel based on the initial correlation information to obtain a parameter estimation value, and a key rate is calculated by combining the parameter estimation value and shot noise;
and a key selection step: extracting the key rate, and selecting the key rate of each sub-channel to obtain a final key;
the transmitting end modulates the coherent state signal by using a Gaussian random number to form a modulated quantum signal, and transmits the quantum signal to the receiving end through an atmospheric channel;
the receiving end divides the local oscillator light through the beam splitter, divides the atmospheric channel into M sub-channels according to the flicker index monitoring of the light intensity of the local oscillator light, obtains the shot noise of each sub-channel, and records as { N }k}k＝1,2,…,MWhere k denotes the kth sub-channel, NkThe shot noise of the kth sub-channel is represented, and M represents the total number of the sub-channels;
the estimated value of the parameter of the atmospheric channel is obtained by the following formula:
Figure FDA0003565485150000011
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003565485150000012
represents the average transmittance of the atmospheric channel;
m' represents the channel transmittance distribution number of the atmospheric subchannel;
Figure FDA0003565485150000013
indicates the channel transmittance TkA corresponding probability;
Figure FDA0003565485150000014
represents the over-noise epsilonkA corresponding probability;
Figure FDA0003565485150000015
representing total noise
Figure FDA0003565485150000016
A corresponding probability;
Figure FDA0003565485150000017
representing modulation variance
Figure FDA0003565485150000018
A corresponding probability;
Figure FDA0003565485150000019
representing the average over-noise of the atmospheric channel;
Figure FDA00035654851500000110
is the signal mean modulation variance;
Figure FDA00035654851500000111
is the total noise of the atmospheric channel;
Figure FDA0003565485150000021
is the total noise of the kth subchannel.
2. The free-space CVQKD system-based parameter estimation method of claim 1 wherein said flicker index is a ratio of a light intensity fluctuation variance of local oscillator light to a light intensity mean square, calculated by:
Figure FDA0003565485150000022
wherein the content of the first and second substances,
Figure FDA0003565485150000023
a flicker index representing the intensity of the local oscillator light;
r represents a deviation value of the centroid of the received beam from the center of the receive aperture;
l represents a transmission distance;
i (r, L) represents the instantaneous local oscillator light intensity under real-time monitoring;
I2(r, L) represents the instantaneous cost under real-time monitoringThe square of the intensity of the oscillator light;
u represents a voltage signal corresponding to the instantaneous light intensity after photoelectric conversion;
<. > indicates that statistical averages were made.
3. The parameter estimation method based on the free-space CVQKD system according to claim 1, characterized in that the transmitting end sends shared data { x ] to the receiving endi}i＝1,2,…,NAfter the receiving end receives the shared data after detecting, extracting the storage data { y of each sub-channeli}i＝1,2,…,NObtaining parameter estimation data
Figure FDA0003565485150000024
The following relationship is satisfied:
Figure FDA0003565485150000025
wherein, tkRepresenting the correlation coefficient of the sending end data and the receiving end data on the k-th sub-channel;
xkrepresents the sender data on the k-th sub-channel;
ykrepresents the receiving end data on the k-th sub-channel;
zkrepresenting noise on the k-th sub-channel, satisfying a mean of zero, variance
Figure FDA0003565485150000026
(ii) a gaussian distribution of;
eta represents the detection efficiency obtained by the pre-selection measurement of the receiving end;
velrepresenting electrical noise resulting from a preselected measurement at the receiving end;
Tkrepresents the transmittance of the k-th sub-channel;
εkrepresents the over-noise of the k-th sub-channel;
Nkis the shot noise of the k-th sub-channel.
4. A method for parameter estimation based on a free-space CVQKD system according to claim 3, characterized in that the estimated values of the parameters are obtained by:
Figure FDA0003565485150000031
wherein the content of the first and second substances,
Figure FDA0003565485150000032
an estimated value representing a correlation coefficient between transmitter data and receiver data on a kth sub-channel;
Figure FDA0003565485150000033
represented on the k-th sub-channel in M groups of data
Figure FDA0003565485150000034
The m groups of data for parameter evaluation are randomly selected;
Figure FDA0003565485150000035
representing the noise z on the k-th sub-channelkAn estimate of the variance of (c);
Figure FDA0003565485150000036
representing the signal modulation variance estimate in the kth subchannel.
5. The free-space CVQKD system-based parameter estimation method according to claim 4, characterized in that the estimated value of the parameter of the kth sub-channel is obtained by:
Figure FDA0003565485150000037
wherein the content of the first and second substances,
Figure FDA0003565485150000038
an estimate value representing a signal modulation variance in the kth subchannel;
Figure FDA0003565485150000039
an estimated value representing the channel transmittance of the kth sub-channel;
Figure FDA00035654851500000310
representing an estimate of the over-noise of the k-th sub-channel,
Figure FDA00035654851500000311
representing an estimate of the total noise of the k-th sub-channel.
6. The method for parameter estimation based on a free-space CVQKD system according to claim 1, characterized in that the kth sub-channel key rate K(k)And the system key rate K is calculated as follows:
Figure FDA00035654851500000312
K＝(1-P)(βIAB-χBE) (6b)
wherein, K(k)Represents the k-th sub-channel key rate;
β represents the reverse negotiation efficiency;
Figure FDA00035654851500000313
representing the mutual information quantity between the sending end and the receiving end on the kth sub-channel;
Figure FDA00035654851500000314
representing the mutual information quantity between the eavesdropper and the receiving end on the kth sub-channel;
k represents the system key rate;
IABrepresenting the mutual information quantity between a sending end and a receiving end in the system;
χBErepresenting the mutual information quantity between an eavesdropper and a receiving end in the system;
Pkrepresenting a communication outage probability for the kth sub-channel;
p represents the system communication outage probability.
7. The method for parameter estimation based on a free-space CVQKD system according to claim 1, wherein the detection of signal light by the receiving end is accomplished by a detector of quantum signals, said detector being a calibrated Homodyne detector; the estimates of the parameter estimates include channel transmittance, channel over-noise, modulation variance, and channel total noise.
8. A parameter estimation system based on a free-space CVQKD system, characterized in that the parameter estimation method based on a free-space CVQKD system as claimed in claim 1 is adopted, and further comprising:
a sub-channel division module: the receiving end separates the optical signal sent by the sending end to obtain signal light and local oscillator light, and divides an atmospheric channel into a plurality of sub-channels through the flicker index of the local oscillator light to obtain shot noise of each sub-channel;
a parameter estimation module: the receiving end detects the signal light to obtain initial correlation information, parameter evaluation is carried out on each sub-channel based on the initial correlation information to obtain a parameter estimation value, and a key rate is calculated by combining the parameter estimation value and shot noise;
a key selection module: and extracting the key rate, and selecting the key rate of each sub-channel to obtain a final key.
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