CN108173647B - Polarization state ambiguity elimination method during incomplete evolution reconstruction - Google Patents

Polarization state ambiguity elimination method during incomplete evolution reconstruction Download PDF

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CN108173647B
CN108173647B CN201711462138.3A CN201711462138A CN108173647B CN 108173647 B CN108173647 B CN 108173647B CN 201711462138 A CN201711462138 A CN 201711462138A CN 108173647 B CN108173647 B CN 108173647B
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polarization state
qber
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evolution
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CN108173647A (en
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周华
王艺敏
赵继勇
苏洋
吴传信
沈荟萍
徐智勇
蒲涛
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Army Engineering University of PLA
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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
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • 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
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Abstract

When a quantum key distribution system is implemented according to protocols of two groups of non-orthogonal bases such as BB84 and the like, the method can be combined with a polarization compensation step to eliminate the polarization state evolution ambiguity reconstructed from the measurement result of quantum communication, and accurate historical data is provided for real-time polarization state prediction and compensation.

Description

Polarization state ambiguity elimination method during incomplete evolution reconstruction
Technical Field
The invention relates to a method for determining evolution history of a certain polarization state according to communication data, in particular to a method for determining a real evolution curve from two possible evolution histories when evolution reconstruction is incomplete in protocols such as BB84 and the like.
Background
Currently, among the known quantum key distribution protocols, the BB84 protocol, the E91 protocol, and the spoofing state protocol above the two protocols use two sets of non-orthogonal bases for encoding and decoding. For a two-dimensional quantum state, the polarization state, requires the use of three sets of non-orthogonal basis measurements to completely resolve the chromatogram. When two sets of non-orthogonal basis measurements are used, ambiguity occurs in the chromatography, so that measures are needed to overcome the ambiguity when polarization compensation is performed based on the result of the chromatography in the quantum key distribution system of the protocol BB84 and the like [ patent 201510228202.6 ]. However, the quantum state reconstructed from the bit error rate and the uncertainty rate of the quantum key distribution is a result obtained after the polarization states in a period of time are approximated to be equal, so that a large error occurs in restoring the history polarization state and predicting the current polarization state. In order to accurately reproduce the time-varying curve of the polarization state, an evolutionary reconstruction method can be adopted. However, when evolutionary reconstruction is performed in a quantum key distribution system implemented using two sets of non-orthogonal bases such as BB84, ambiguity results also occur, and polarization state prediction and compensation cannot be performed based on evolutionary reconstruction.
Disclosure of Invention
The invention aims to eliminate ambiguity of polarization evolution reconstruction in a quantum key distribution system realized by using two groups of non-orthogonal bases according to protocols such as BB84 and the like, and determine an actual evolution history so as to smoothly realize polarization state prediction and compensation based on the evolution history.
The technical scheme of the invention is as follows:
the invention provides a method for eliminating ambiguity of a polarization state when evolution reconstruction is incomplete, which comprises the following steps:
(a) the sending end and the receiving end use two groups of non-orthogonal bases to carry out quantum communication, and the polarization state to be compensated is recorded as | H >;
(b) obtaining two sets of base measurements | H of the system during the current compensation period>Respectively denoted as ρ|H>1(t)、ρ|H>2(t)；
(c) From rho|H>1(t) and ρ|H>2(t) obtaining a third set of basis measurements | H that are non-orthogonal to the two sets of basis measurements used by the system during the same time period>To obtain two possible results
Figure BDA0001530513930000021
And
Figure BDA0001530513930000022
(d) according to two sets of operator mean functions respectively
Figure BDA0001530513930000023
And
Figure BDA0001530513930000024
obtaining two possible time-varying polarization states | X in the same time periodA(t)>And | XB(t)>；
(e) Recording the quantum bit error rate QBER obtained by eavesdropping detection in the current compensation periodpOptionally | XA(t)>Or | XB(t)>Is true in the preceding periodAccording to the evolution history, the polarization state prediction and compensation are carried out, and the selected real evolution history is marked as | X (t)>The unselected time-varying polarization state is denoted as | X' (t)>；
(f) In the next compensation period, recording the quantum bit error rate obtained by eavesdropping detection after the previous compensation as QBERnAnd obtaining two new possible time-varying polarization states | Y according to the steps (b) to (d)A(t)>And | YB(t)>；
(g) If QBERnGreater than QBERpThen | X' (t)>Determining evolution history as true and changing to | X (t)>(ii) a Else, | X (t)>No change is made;
(h) compare | YA(t)>And | YB(t)>And updated | X (t)>Coincidence of function values in coincidence periods, if YA(t)>And | X (t)>High degree of coincidence, will | YA(t)>Determining a new evolution history and changing to | X (t)>Will | YB(t)>Changed as | X' (t)>(ii) a If | YB(t)>And | X (t)>High degree of coincidence, will | YB(t)>Determining a new evolution history and changing to | X (t)>Will | YA(t)>Changed as | X' (t)>；
(i) QBERnChanged as QBERpAccording to | X (t)>Predicting and compensating the polarization state in the current compensation period;
(j) and (f) continuing to execute the step.
Further, in the step (b), if ρ|H>1(t) or ρ|H>2(t) failing to acquire, then go to step (a) to continue execution.
Further, in step (h), | Y is comparedA(t)>And | YB(t)>And | X (t)>During the coincidence period t1，t2]The contact ratio method of the function values is as follows: calculating an integral
Figure BDA0001530513930000031
Obtain the value sigmaACalculating an integral
Figure BDA0001530513930000032
Obtain the value sigmaBIf σ isAGreater than sigmaBThen determine | YA(t)>And | X (t)>High contact ratio, otherwise, determine | YB(t)>And | X (t)>The contact ratio is high.
Further, in step (h), | Y is comparedA(t)>And | YB(t)>And | X (t)>During the coincidence period t1，t2]The contact ratio method of the function values is as follows: at [ t ]1，t2]Optionally N time instants tau1…τNCalculating a sum
Figure BDA0001530513930000033
Obtain the numerical value
Figure BDA0001530513930000035
Calculating a sum
Figure BDA0001530513930000034
Obtain the numerical value
Figure BDA0001530513930000036
If it is not
Figure BDA0001530513930000037
Is greater than
Figure BDA0001530513930000038
Determine | YA(t)>And | X (t)>High contact ratio, otherwise, determine | YB(t)>And | X (t)>The contact ratio is high.
Further, N is equal to or greater than 100.
The invention has the beneficial effects that:
in the invention, when the quantum key distribution system is realized by using two groups of non-orthogonal base protocols according to BB84 and the like, the method can eliminate the polarization state evolution ambiguity reconstructed from the measurement result of quantum communication by combining the step of polarization compensation, and provides exact historical data for real-time polarization state prediction and compensation.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Detailed Description
Preferred embodiments of the present invention will be described below. While the preferred embodiments of the present invention are shown in the examples, it should be understood that the present invention may be embodied in various forms and should not be limited by the embodiments set forth herein.
A quantum key distribution system realized according to BB84 protocol, the system uses two groups of non-orthogonal bases { | H >, | V > }, { | + >, and | - >, to encode and decode, and adopts a polarization state ambiguity elimination method when evolution reconstruction is incomplete in the process of polarization state prediction and compensation according to the evolution reconstruction result, which comprises the following steps:
(a) quantum communication is carried out between the sending end and the receiving end, and the reconstructed polarization state is recorded as | H >;
(b) obtaining | H in the current compensation period><H | and | +><+ | two operators measure | H>Is taken as p|H>1(t)、ρ|H>2(t); if ρ|H>1(t) or ρ|H>2(t) if the acquisition fails, the step (a) is continued to be executed;
(c) according to rho|H>1(t) and ρ|H>2(t) obtaining a circular polarization base { | R>，|L>Contained operator | R><R | Measure | H>To obtain two possible results
Figure BDA0001530513930000041
And
Figure BDA0001530513930000042
(d) according to two sets of operator mean functions respectively
Figure BDA0001530513930000043
And
Figure BDA0001530513930000044
obtaining two possible time-varying polarization states | X in the same time periodA(t)>And | XB(t)>；
(e) Record the current compensation weekQuantum error rate QBER obtained by phase eavesdropping detectionpOptionally | XA(t)>Or | XB(t)>Predicting and compensating the true evolution history in the period according to the polarization state, and recording the selected true evolution history as | X (t)>The unselected time-varying polarization state is denoted as | X' (t)>；
(f) In the next compensation period, recording the quantum bit error rate obtained by eavesdropping detection after the previous compensation as QBERnAnd obtaining two new possible time-varying polarization states | Y according to the steps (b) to (d)A(t)>And | YB(t)>；
(g) If QBERnGreater than QBERpThen | X' (t)>Determining evolution history as true and changing to | X (t)>(ii) a Else, | X (t)>No change is made;
(h) remember | YA(t)>And | YB(t)>And | X (t)>Coincidence time period of [ -T, 0 [)]Taking 1 point every T/100 in the time interval, and taking 100 points { -T + T/100, …, Ti…, 0}, calculating two summations
Figure BDA0001530513930000051
And
Figure BDA0001530513930000052
respectively obtain the numerical values
Figure BDA0001530513930000053
Sum value
Figure BDA0001530513930000054
If it is not
Figure BDA0001530513930000055
Is greater than
Figure BDA0001530513930000056
Then | YA(t)>Determining a new evolution history and changing to | X (t)>Will | YB(t)>Changed as | X' (t)>Otherwise will | YB(t)>Determining a new evolution history and changing to | X (t)>Will | YA(t)>Changed as | X' (t)>；
(i) QBERnChanged as QBERpAccording to | X (t)>And predicting and compensating the polarization state in the current compensation period.
(j) And (f) continuing to execute the step.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims (3)

1. A method for eliminating ambiguity of a polarization state when evolution reconstruction is incomplete is characterized in that: it comprises the following steps:
(a) the sending end and the receiving end use two groups of non-orthogonal bases to carry out quantum communication, and the polarization state to be compensated is recorded as | H >;
(b) obtaining two sets of base measurements | H of the system during the current compensation period>Respectively denoted as ρ|H>1(t)、ρ|H>2(t)；
(c) From rho|H>1(t) and ρ|H>2(t) obtaining a third set of basis measurements | H that are non-orthogonal to the two sets of basis measurements used by the system during the same time period>To obtain two possible results
Figure FDA0002809570770000011
And
Figure FDA0002809570770000012
(d) according to two sets of operator mean functions respectively
Figure FDA0002809570770000013
And
Figure FDA0002809570770000014
obtain two in the same time periodPossible time-varying polarization state | XA(t)>And | XB(t)>；
(e) Recording the quantum bit error rate QBER obtained by eavesdropping detection in the current compensation periodpOptionally | XA(t)>Or | XB(t)>Predicting and compensating the true evolution history in the period according to the polarization state, and recording the selected true evolution history as | X (t)>The unselected time-varying polarization state is denoted as | X' (t)>；
(f) In the next compensation period, recording the quantum bit error rate obtained by eavesdropping detection after the previous compensation as QBERnAnd obtaining two new possible time-varying polarization states | Y according to the steps (b) to (d)A(t)>And | YB(t)>；
(g) If QBERnGreater than QBERpThen | X' (t)>Determining evolution history as true and changing to | X (t)>(ii) a Else, | X (t)>No change is made;
(h) compare | YA(t)>And | YB(t)>And updated | X (t)>Coincidence of function values in coincidence periods, if YA(t)>And | X (t)>High degree of coincidence, will | YA(t)>Determining a new evolution history and changing to | X (t)>Will | YB(t)>Changed as | X' (t)>(ii) a If | YB(t)>And | X (t)>High degree of coincidence, will | YB(t)>Determining a new evolution history and changing to | X (t)>Will | YA(t)>Changed as | X' (t)>；
(i) QBERnChanged as QBERpAccording to | X (t)>Predicting and compensating the polarization state in the current compensation period;
(j) go to step (f) to continue execution;
in step (h), Y is comparedA(t)>And | YB(t)>And | X (t)>During the coincidence period t1，t2]The contact ratio method of the function values is as follows: calculating an integral
Figure FDA0002809570770000021
Obtain the value sigmaACalculating an integral
Figure FDA0002809570770000022
Obtain the value sigmaBIf σ isAGreater than sigmaBThen determine | YA(t)>And | X (t)>High contact ratio, otherwise, determine | YB(t)>And | X (t)>The contact ratio is high;
in step (h), Y is comparedA(t)>And | YB(t)>And | X (t)>During the coincidence period t1，t2]The contact ratio method of the function values is either: at [ t ]1，t2]Optionally N time instants tau1...τNCalculating a sum
Figure FDA0002809570770000023
Obtain the numerical value
Figure FDA0002809570770000024
Calculating a sum
Figure FDA0002809570770000025
Obtain the numerical value
Figure FDA0002809570770000026
If it is not
Figure FDA0002809570770000027
Is greater than
Figure FDA0002809570770000028
Determine | YA(t)>And | X (t)>High contact ratio, otherwise, determine | YB(t)>And | X (t)>The contact ratio is high.
2. The method for polarization ambiguity elimination when evolving reconstruction is incomplete as claimed in claim 1, wherein: in step (b), if ρ|H>1(t) or ρ|H>2(t) failing to acquire, then go to step (a) to continue execution.
3. The method for polarization ambiguity elimination when evolving reconstruction is incomplete as claimed in claim 1, wherein; n is more than or equal to 100.
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