CN108540284B - Continuous variable quantum key distribution post-processing heterodyne detection phase compensation method - Google Patents

Continuous variable quantum key distribution post-processing heterodyne detection phase compensation method Download PDF

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CN108540284B
CN108540284B CN201810559087.4A CN201810559087A CN108540284B CN 108540284 B CN108540284 B CN 108540284B CN 201810559087 A CN201810559087 A CN 201810559087A CN 108540284 B CN108540284 B CN 108540284B
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郭弘
彭翔
陈子扬
张一辰
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Abstract

The invention discloses a continuous variable quantum key distribution post-processing heterodyne detection phase compensation method. The method comprises the following steps: 1) a receiving end Bob receives the quantum state prepared by the sender Alice and blocks data obtained by heterodyne detection according to a set proportion; 2) bob sends the phase compensation data to Alice; 3) calculating the phase drift of the X component and the phase drift of the P component of the two adjacent phase compensation data according to the two adjacent phase compensation data and the corresponding sending data recorded by the Alice during the quantum state preparation; 4) alice calculates the phase drift of the X component of the data to be compensated between the corresponding sending data recorded during the quantum state preparation according to the phase drift of the two adjacent phase compensation data
Figure DDA0001682725990000011
The phase shift θ of the P component; 5) alice base on
Figure DDA0001682725990000012
And theta performs phase rotation on X, P components of the data to be compensated to obtain the data after phase compensation.

Description

Continuous variable quantum key distribution post-processing heterodyne detection phase compensation method
Technical Field
The invention relates to the technical field of quantum information, in particular to a data structure method for heterodyne detection phase compensation by post-processing in a continuous variable quantum key distribution system.
Background
Generally, after a signal is transmitted over a long distance, particularly when the signal is transmitted in an atmospheric channel, the phase of the signal light may shift to some extent due to the influence of the channel. For the receiver of the signal, it is necessary to perform phase compensation on the signal to obtain accurate information. In the continuous variable quantum key distribution protocol based on the optical fiber, a phase reference signal is generally added when a signal is sent, and a feedback voltage can be generated to a phase modulator on an intrinsic optical path of a receiving end by measuring the phase reference signal, so that real-time phase compensation is realized. In the atmospheric channel, the phase compensation is more complicated.
The phase compensation method using the electrical method is limited in accuracy of the electrical method by the accuracy of the digital and analog circuits, and the compensation accuracy is limited due to the extra electrical noise introduced during the compensation process.
Disclosure of Invention
In view of the technical problems in the prior art, an object of the present invention is to provide a method for performing phase compensation by post-processing in a continuous variable quantum key distribution protocol for heterodyne detection. The invention compensates the phase of the signal by using the algorithm in the post-processing of the signal, not only improves the precision of the phase compensation, but also reduces the complexity of a physical implementation system of a receiving end, greatly improves the flexibility and the portability of the phase compensation, and ensures that the phase compensation can be suitable for various external environments without making great data adjustment.
The method of the invention processes data, thereby avoiding the limitation brought by the problems, improving the precision of phase compensation and reducing the complexity of a physical realization system of a receiving end. In addition, the method has the advantages of flexible structure and strong portability because the proportion of the compensation data can be specifically adjusted according to the phase drift rate without changing the format of the whole data structure according to different experimental environments.
Aiming at the purposes, the technical scheme adopted by the invention is as follows:
a method for heterodyne detection phase compensation by post-processing is suitable for a continuous variable quantum key distribution system and comprises the following steps:
1) in a quantum key distribution system in which the data detected by the heterodyne are continuous variables, Bob selects data used for phase compensation according to a certain proportion from the data obtained by heterodyne detection, and the blocking proportion of the common data is that the phase compensation data and the data to be compensated are blocked in a ratio of 1: 9; the data after being partitioned are distributed at intervals according to the phase compensation data and the data to be compensated, and the phase drift of each block of data is constant; in addition, the phase compensation effect can also be optimized by selecting data with different proportions as phase compensation data according to different specific environment tests (the phase drift rate of the system needs to be determined according to specific experimental environments).
2) Bob sends the phase compensation data to Alice;
3) respectively calculating the phase drift of the phase compensation data of the X component (regular coordinate) data and the P component (regular momentum) data which are adjacent twice by Alice according to the phase compensation data and the data in the hand;
4) respectively calculating the phase drift of the data to be compensated between the adjacent X data and the data to be compensated between the adjacent P data by Alice according to the phase drift of the two adjacent phase compensation data;
5) and respectively carrying out phase rotation on the data X and the data P to be compensated according to the phase drift of the data to be compensated by Alice to obtain data after phase compensation.
Further, the data obtained by Bob through heterodyne detection in the step 1) comprises X component data XBAnd P component data PB。
Further, the data in the hand in step 3) refers to data information recorded by Alice during quantum state preparation, and includes X component (regular coordinate) data XAAnd P component (regular momentum) data PA。
Further, the method for calculating the phase drift of each phase compensation data in step 3) comprises the following steps:
3-1) Alice calculates the data X in the hand respectivelyAWith corresponding phase compensation data XBAnd PBTo obtain cov (X)A,XB) And cov (X)A,PB) (ii) a Data XAWith corresponding phase compensation data XBAnd PBIs data generated at the same time, in continuous variable quantum key distribution, if Bob uses heterodyne detection, Bob generates a set of data X each timeBAnd PBWill generate a set of X corresponding to AliceAAnd PA。
3-2) cov (X) obtained by the above calculationA,XB) And cov (X)A,PB) Calculating a phase drift of X component data of the phase compensation data
Figure GDA0002629755340000021
3-3) Alice calculates the data P in the hand respectivelyAAnd phase compensation data XBAnd PBTo obtain cov (P)A,XB) And cov (P)A,PB)；
3-4) cov (P) obtained from the above calculationA,XB) And cov (P)A,PB) Calculating a phase drift θ of the P component data of the phase compensation data.
Further, cov (X) described in step 3-1)A,XB) And cov (X)A,PB) The calculation formula of (2) is as follows:
Figure GDA0002629755340000022
Figure GDA0002629755340000031
wherein
Figure GDA0002629755340000032
The phase drift of the X component data, which is phase compensation data, t represents a scaling factor, V, introduced during signal transmission due to noise and the likeAAnd the variance of modulation data at the Alice terminal is shown.
Further, the phase of the phase compensation data in step 3-2) is shifted
Figure GDA0002629755340000033
The calculation formula of (2) is as follows:
Figure GDA0002629755340000034
cov therein(XA,PB) As data X in the handAAnd phase compensation data PBCovariance of (2), cov (X)A,XB) As data X in the handAAnd phase compensation data XBThe covariance of (a).
Further, cov (P) described in step 3-3)A,XB) And cov (P)A,PB) The calculation formula of (2) is as follows:
cov(PA,XB)＝tVAsin(θ)
cov(PA,PB)＝tVAcos(θ)
where θ is the phase shift of the P component data of the phase compensation data, t represents the scaling factor introduced by noise and the like during signal transmission, and VAThe variance of data sent by Alice side is shown.
Further, the calculation formula of the phase shift θ of the P component data of the phase compensation data in step 3-4) is:
Figure GDA0002629755340000035
cov (P) thereinA,XB) For compensating the data X for the phaseBAnd data P in handACovariance of (2), cov (P)A,PB) For compensating the data PBAnd data P in handAThe covariance of (a).
Further, if it is assumed that the data X phase drifts of the two adjacent phase compensation data in step 3) are respectively
Figure GDA0002629755340000036
The phase drift of the data to be compensated between the data sent corresponding to the two adjacent phase compensation data recorded by Alice during the quantum state preparation in the step 4) is
Figure GDA0002629755340000037
Further, if it is assumed that the two adjacent phase compensations in step 3) are performedThe data P of the data has a phase shift of theta1、θ2If so, the phase drift of the data to be compensated between the sending data corresponding to the two adjacent phase compensation data recorded by Alice during the quantum state preparation in the step 4) is theta0＝0.5(θ1+θ2)。
Further, the data to be compensated X, P in step 5) is calculated as follows to perform phase rotation, so as to obtain data X 'and P' after phase compensation;
Figure GDA0002629755340000041
Figure GDA0002629755340000042
wherein
Figure GDA0002629755340000043
For the phase drift, theta, of the data to be compensated between the two adjacent X phase compensation data0And compensating the phase drift of the data to be compensated between the two adjacent data P phases.
The invention has the beneficial effects that:
the invention provides a method for heterodyne detection phase compensation by utilizing a post-processing mode, which is suitable for a continuous variable quantum key distribution system. The method reduces the complexity of a physical realization system of a receiving end by realizing phase compensation in the post-processing of a continuous variable quantum key distribution system; the flexibility and the portability of phase compensation are improved; meanwhile, as the method carries out phase compensation in a data processing mode, compared with the prior mode of passing through a circuit, the method improves the precision of phase compensation.
Drawings
FIG. 1 is a diagram illustrating the position relationship between phase compensation data and data to be compensated according to the present invention.
Fig. 2 is a flowchart of a method for performing heterodyne detection phase compensation by post-processing according to the present invention.
Detailed Description
In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.
In the continuous variable quantum key distribution system, Gaussian modulation data loaded on two regular components by Alice is assumed to be (X)A,PA) And transmitting the prepared quantum state to a receiving end Bob by Alice in a quantum channel. After receiving the quantum state, Bob detects the quantum state and obtains the received data, wherein heterodyne detection is one of the commonly used detection methods. In the heterodyne detection method, data detected by the Bob end is assumed to be XBAnd PBBecause the quantum state inevitably introduces noise and phase drift when passing through the quantum channel and two heterodyne detectors are needed for heterodyne detection, the receiving end is considered to be connected to the XBAnd PBRespectively, are
Figure GDA0002629755340000044
And θ, then (X)A,PA) And XBOr PBThere is a relationship as shown in equation (1).
Figure GDA0002629755340000045
Figure GDA0002629755340000046
Wherein the content of the first and second substances,
Figure GDA0002629755340000047
in order to shift the phase of data X, θ is the phase shift of data P, ξ and ξ' are noise, and t represents a scaling factor introduced during signal transmission due to noise and the like. In the invention, the sending end Alice needs to rotate the data X corresponding to the data in the hand by the phase
Figure GDA0002629755340000051
The data P is rotated by the phase θ to counteract the phase drift. Since the speed of phase shift is a slow process to the data transmission rate, the phase shift of the data can be considered to be a constant value in a short time, so that the data can be divided into blocks, and phase compensation is performed separately for each block of data, and the phase shift in each block of data is considered to be constant. Referring to fig. 1, for data obtained by heterodyne detection, Bob selects a portion of the data in a certain proportion for phase compensation, called phase compensation data. And the rest of the data is reserved as the data to be compensated. Suppose Bob measures an X component of
Figure GDA0002629755340000052
Measured P component of
Figure GDA0002629755340000053
Due to XA，PAξ are independent of one another, so that this part of the data corresponds to the corresponding part
Figure GDA0002629755340000054
And
Figure GDA0002629755340000055
the covariance was found to cov (X)A,XB) And cov (X)A,PB) As shown in equation (2).
And can calculate the phase compensation phase of the Alice terminal
Figure GDA0002629755340000056
The tangent of (c) is as shown in equation (3).
Figure GDA0002629755340000057
Figure GDA0002629755340000058
Figure GDA0002629755340000059
Covariance cov (P) may also be calculatedA,XB) And cov (P)A,PB) As shown in equation (4). And the tangent value of the phase θ of the phase compensation at the Alice end can be calculated as shown in equation (5).
cov(PA,XB)＝tVAsin(θ)
cov(PA,PB)＝tVAcos(θ) (4)
Figure GDA00026297553400000510
According to the above formulas (2) and (3) and
Figure GDA00026297553400000511
and
Figure GDA00026297553400000512
the positive and negative relations of (2) can be calculated to calculate the phase drift of the data X
Figure GDA00026297553400000513
The phase shift θ of the data P can also be calculated. The phase drift calculation results of the phase compensation data of two adjacent data X are respectively
Figure GDA00026297553400000514
The phase drift calculation results of the phase compensation data of two adjacent data P are respectively theta1、θ2. For a linear circuit, the phase drift process can be understood according to simple linearity, and the phase drifts of the data to be compensated between the sending data corresponding to the two adjacent phase compensation data recorded when Alice performs quantum state preparation can be obtained as
Figure GDA00026297553400000515
θ0＝0.5(θ1+θ2)。
The present invention is explained below by referring to an embodiment, referring to fig. 2, the method steps of the embodiment include:
1) bob selects data used as phase compensation according to a certain proportion from data obtained by heterodyne detection, and uses the phase compensation data XB、PBAnd sending the data to Alice. For example, 500 out of every 5000 data are selected as phase compensation data.
2) Respectively calculating the phase compensation data X by AliceB、PBAnd hand data XAAnd data PACovariance of cov (X)A,XB)、cov(XA,PB)、cov(PA,XB)、cov(PA,PB). And according to covariance cov (X)A,XB) And cov (X)A,PB) And the above formula (3), using an inverse trigonometric function and
Figure GDA0002629755340000061
and
Figure GDA0002629755340000062
calculating the phase drift of the phase compensation data
Figure GDA0002629755340000063
According to covariance cov (P)A,XB) And cov (P)A,PB) And the above equation (5), calculating the phase shift θ of the phase compensation data using the inverse trigonometric function and the positive-negative relationship of cos (θ) and sin (θ).
3) The phase drift calculation results of the two adjacent data X phase compensation data are respectively
Figure GDA0002629755340000064
The phase drift of the data to be compensated between the data sent corresponding to the two adjacent phase compensation data recorded by Alice during the quantum state preparation is
Figure GDA0002629755340000065
The phase drift calculation results of the phase compensation data of two adjacent data P are respectively theta1、θ2If so, the phase drift of the data to be compensated between the sending data corresponding to the two adjacent phase compensation data recorded by Alice during the quantum state preparation is θ equal to 0.5(θ ═ 0.5)1+θ2)。
4) And (3) performing calculation as shown in the following formulas (6) and (7) on the data to be compensated X, P between the sending data corresponding to the two adjacent phase compensation data recorded during quantum state preparation by Alice, performing phase rotation to obtain data X 'and P' after phase compensation, and storing the data X 'and P' as data of Alice for parameter estimation and subsequent post-processing.
Figure GDA0002629755340000066
Figure GDA0002629755340000067
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and a person skilled in the art can make modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the present invention, and the scope of the present invention should be determined by the claims.

Claims (10)

1. A continuous variable quantum key distribution post-processing heterodyne detection phase compensation method comprises the following steps:
1) a receiving end Bob receives the quantum state prepared by the sender Alice, detects the received quantum state through heterodyne detection, and then blocks data obtained through heterodyne detection according to a set proportion to obtain data of phase compensation data and data to be compensated which are distributed at intervals;
2) bob sends each phase compensation data to Alice; the phase compensation data comprises X component data and P component data;
3) according to the ith phase compensation data and corresponding sending data recorded by Alice during quantum state preparation, the Alice calculates the phase drift of the X component data in the ith phase compensation data
Figure FDA0002629755330000011
P component data phase drift θi(ii) a According to the i +1 th phase compensation data and corresponding sending data recorded by Alice during quantum state preparation, the Alice calculates the phase drift of the X component data in the i +1 th phase compensation data
Figure FDA0002629755330000012
P component data phase drift θi+1；
4) Alice compensates the phase drift of the X component data in the data according to the two adjacent phases
Figure FDA0002629755330000013
Calculating X component data X of data to be compensated between sending data corresponding to the two adjacent phase compensation data recorded when Alice carries out quantum state preparationDPhase drift of
Figure FDA0002629755330000014
According to the phase shift theta of P component data in two adjacent phase compensation datai、θi+1Calculating P component data P of data to be compensated between the data to be compensated and the data sent corresponding to the two adjacent phase compensation data recorded when the quantum state preparation is carried out by AliceDThe phase drift of θ;
5) alice drifts according to phase
Figure FDA0002629755330000015
For the X component data XDPerforming phase rotation on the P component data P according to the phase drift thetaDAnd carrying out phase rotation to obtain data after phase compensation.
2. The method of claim 1, wherein the quantum state is prepared by loading gaussian modulation data on two canonical components.
3. Method according to claim 1 or 2, characterized in that the phase drift is calculated
Figure FDA0002629755330000016
The method comprises the following steps: alice calculates XAAnd XBCovariance of cov (X)A,XB)、XAAnd PBCovariance of cov (X)A,PB) Wherein X isBFor X component data, X, in the phase compensation data received by Bob at the ith timeAFor Alice to interact with X in the transmitted data recorded during quantum state preparationBCorresponding X component data, PBP component data in the phase compensation data received by Bob at the ith time; then according to cov (X)A,XB) And cov (X)A,PB) Calculating the phase drift
Figure FDA0002629755330000017
4. The method of claim 3, wherein the method is based on a formula
Figure FDA0002629755330000018
Calculating the phase drift
Figure FDA0002629755330000019
5. The method of claim 1 or 2, wherein the phase drift θ is calculatediThe method comprises the following steps: alice calculates PAAnd XBCovariance of cov (P)A,XB)、PAAnd PBCovariance of cov (P)A,PB) Wherein P isBCompensating for the phase received by Bob at the i-th timeData of P component in data, PAFor Alice to record the data in the sending data during the quantum state preparation and PBCorresponding P component data, XBThe data of the X component in the phase compensation data received by Bob at the ith time; then according to cov (P)A,XB) And cov (P)A,PB) Calculating the phase drift θi。
6. The method of claim 5, wherein the method is based on a formula
Figure FDA0002629755330000021
Calculating the phase drift θi。
7. The method of claim 1 or 2, wherein the phase drift
Figure FDA0002629755330000022
The phase shift θ is 0.5(θ)i+θi+1)。
8. The method of claim 1, wherein in step 5), a formula is used
Figure FDA0002629755330000023
For the data XDPerforming phase rotation to obtain data X' after phase compensation; using formulas
Figure FDA0002629755330000024
For the data PDAnd performing phase rotation to obtain data P' after phase compensation.
9. The method of claim 1, wherein the set ratio is 1:9, that is, the ratio of the phase compensation data to the data to be compensated in step 1) is 1: 9.
10. The method of claim 1, wherein Alice transmits the prepared quantum states in a quantum channel to a receiving end Bob.
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