CN112929156B - Calculation method for coding error rate of quantum key generation system - Google Patents

Calculation method for coding error rate of quantum key generation system Download PDF

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CN112929156B
CN112929156B CN201911241671.6A CN201911241671A CN112929156B CN 112929156 B CN112929156 B CN 112929156B CN 201911241671 A CN201911241671 A CN 201911241671A CN 112929156 B CN112929156 B CN 112929156B
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Beijing Zhongchuangwei Nanjing Quantum Communication 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
    • 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
    • H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding

Abstract

The application provides a method for calculating the code forming error rate of a quantum key generation system, which can be used for calculating the code forming error rate of a simplified BB84 protocol and accordingly provides the code forming rate of a communication system, which does not need to depend on a basic detection efficiency condition, and has a more compact estimated value of the phase error rate and a simpler calculation mode. The method mainly comprises the following steps: step 1: the sender and the receiver of the quantum key distribution carry out preparation, transmission and measurement of quantum states according to a simplified BB84 protocol; step 2: comparing the basis vectors of the sender and the receiver; and step 3: the sender and the receiver correct errors to obtain the bit error rate measured by the receiver by using the Z basis vector; and 4, step 4: calculating the phase error rate measured by the Z basis vector at the receiving party; and 5: and carrying out privacy amplification on the key after discarding the basis vector information to obtain the resultant code rate.

Description

Calculation method for coding error rate of quantum key generation system
Technical Field
A computing method for a code forming error rate of a quantum key generation system is used for solving the problem of dependence on detection efficiency of a receiver detection unit in the prior art, improving estimation of a related error rate and simplifying a computing mode.
Background
The quantum key distribution system, which is one of the most promising technologies in quantum information technology, mainly comprises two parts: the device comprises a hardware part, a data processing part and a data processing part, wherein the hardware part comprises a sending device, a receiving device and a measuring device; second is post-processing of software and data. In the quantum key distribution protocol, a sender prepares a quantum state, a receiver receives and detects the quantum state from a quantum channel (or a shared channel), the two parties exchange necessary information through a public channel, data post-processing is carried out, error correction, privacy amplification and the like are included, and finally the two parties obtain a key.
More recently, a simplified BB84 protocol (simplified BB84 protocol, d.rusca, a.boaron, m.curty, a.martin, and h.zbinden, phys.rev.a 98,052336(2018)) has been proposed. The simplified BB84 protocol requires that three different quantum states be prepared at the transmitter and tested at the receiver. The protocol further simplifies the experimental difficulty:
a sender of quantum key distribution randomly selects a Z basis vector and an X basis vector to prepare a quantum state; wherein the probability of selecting the Z basis vector is p, and the probability of selecting the X basis vector is 1-p; when a Z basis vector is selected, a sender randomly obtains a prepared quantum state |0> and a prepared quantum state |1>, the probability of preparing the quantum state |0> is p/2, and the probability of preparing the quantum state |1> is p/2; when the X basis vector is selected, the sender always prepares the quantum state | + >; a receiving party for quantum key distribution randomly selects a Z basis vector and an X basis vector to measure a quantum state; wherein the probability of selecting the Z basis vector is q, and the probability of selecting the X basis vector is 1-q; when the receiving party selects the Z basis vector, measuring |0>, |1 >; when the receiver selects the X basis vector, | - > is measured.
However, simplifying the BB84 protocol requires that the measurement basis vector independent probing efficiency condition be satisfied, which is difficult to satisfy in some quantum key distribution systems. For example, for a time-phase encoded quantum key distribution system that is selected based on a passive basis vector, the detection efficiency of the phase basis vector is typically 3dB less than the detection efficiency of the time basis vector.
Meanwhile, when the scheme is used for estimating the phase error rate, the existing calculation formula is complex, and the estimated value of the phase error rate is large under the condition of long-distance quantum key distribution, so that the safety code rate is seriously reduced.
Disclosure of Invention
In order to solve the problems, the application provides a simplified safe code rate calculation mode of the BB84 protocol, which does not need to depend on a basic detection efficiency condition, and the estimated value of the phase error rate is more compact and the calculation mode is simpler.
Step 1: the sender and the receiver of the quantum key distribution system carry out preparation, transmission and measurement of quantum states according to a simplified BB84 protocol;
preferably, the quantum state transmission and preparation in step 1 is performed as follows: the sender prepares not less than three quantum states, but the three quantum states are prepared strictly according to the requirements of a simplified BB84 protocol; when measuring the received quantum state, the receiving party measures the quantum state prepared by the transmitting party according to the requirement of the simplified BB84 protocol strictly according to the requirement of the simplified BB84 protocol strictly.
Step 2: comparing the basis vectors of the sender and the receiver;
and step 3: the data processing module sender and receiver of the quantum key distribution system carry out error correction to obtain the bit error rate measured by the receiver by using the Z basis vector
Figure BDA0002306423230000011
Figure BDA0002306423230000012
Wherein E iszThe bit error rate measured with the Z basis vector for the receiver can be measured directly.
And 4, step 4: the data processing module of the quantum key distribution system calculates the phase error rate measured by the Z basis vector of the receiver
Figure BDA0002306423230000021
Figure BDA0002306423230000022
Wherein, Ya,-(a is 0,1) represents that the sender sends out quantum state | a by adopting Z basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication can be directly measured in real time during actual communication. Y is+,-Represents that the sender sends quantum state | +by adopting X basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication can be directly measured in real time during actual communication.
Wherein, YXXThe quantum state is prepared by the X basis vector for the sender, and the Yield (Yield) obtained by the X basis vector measurement for the receiver can be obtained by calculation or can be directly obtained by real-time measurement during actual communication. Y isZXThe quantum state is prepared by the Z basis vector for the sender, and the Yield (Yield) measured by the X basis vector for the receiver can be obtained by calculation or can be obtained by real-time measurement during communication.
And 5: the data processing module of the quantum key distribution system carries out privacy amplification on the key after discarding the basis vector information to obtain a code rate:
Figure BDA0002306423230000023
wherein f is an error correction coefficient,
Figure BDA0002306423230000024
the yield of the optical pulse with the intensity of alpha is measured by a base vector of a sending party and a base vector of b of a receiving party,
Figure BDA0002306423230000025
the bit error rate measured by the b-base vector is used by the receiving side for transmitting the optical pulse with the intensity of alpha by the a-base vector by the transmitting side.
Figure BDA0002306423230000026
Figure BDA0002306423230000027
Figure BDA0002306423230000028
Figure BDA0002306423230000029
Figure BDA00023064232300000210
The yield of n photon state measured by a base vector of a transmitting party and a base vector of b of a receiving party is obtained. Mu, v, omega denote the average photon number of the three different light pulses used by the sender.
Wherein, the steps 3 and 4 in the application can be performed in an alternative order or simultaneously.
The scheme has the following advantages:
1. the scheme does not depend on the basic detection efficiency condition.
2. The estimated value of the phase error rate is more compact, the calculation method is simpler, the estimated value can be obtained through actual measurement, and finally the bit rate of the quantum communication system is improved.
3. The calculation formulas of the bit error rate and the phase error rate provided by the scheme are also suitable for the known four-state protocol.
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In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the implementation of the present solution;
Detailed Description
In order to make the aforementioned objects, features and advantages of the present application more comprehensible, the present application is described in further detail with reference to the accompanying drawings and the detailed description.
The application provides a computing method for the code forming error rate of a quantum key generation system, and the computing result of the method is more compact, so that the aim of improving the code forming rate of the system is fulfilled.
[ example 1 ]
Step 1: the sender and the receiver of the quantum key distribution system carry out preparation, transmission and measurement of quantum states according to a simplified BB84 protocol;
step 2: comparing the basis vectors of the sender and the receiver;
and step 3: the data processing module sender and receiver of the quantum key distribution system carry out error correction to obtain the bit error rate measured by the receiver by using the Z basis vector
Figure BDA0002306423230000031
Figure BDA0002306423230000032
Wherein E iszThe bit error rate measured with the Z basis vector for the receiver can be measured directly.
And 4, step 4: the data processing module of the quantum key distribution system calculates the phase error rate measured by the Z basis vector at the receiving party
Figure BDA0002306423230000033
Figure BDA0002306423230000034
Wherein, Ya,-(a is 0,1) represents that the sender sends out quantum state | a by adopting Z basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication can be directly measured in real time during actual communication. Y is+,-Represents that the sender sends quantum state | +by adopting X basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication can be directly measured in real time during actual communication.
Wherein, YXXThe quantum state is prepared by the X basis vector for the sender, and the Yield (Yield) obtained by the X basis vector measurement for the receiver can be obtained by calculation or can be directly obtained by real-time measurement during actual communication. Y isZXThe quantum state is prepared by the Z basis vector for the sender, and the Yield (Yield) measured by the X basis vector for the receiver can be obtained by calculation or can be obtained by real-time measurement during communication.
And 5: the data processing module of the quantum key distribution system carries out privacy amplification on the key after discarding the basis vector information to obtain a code rate:
Figure BDA0002306423230000035
wherein f is an error correction coefficient,
Figure BDA0002306423230000036
the yield of the optical pulse with the intensity of alpha is measured by a base vector of a sending party and a base vector of b of a receiving party,
Figure BDA0002306423230000037
the bit error rate measured by the b-base vector is used by the receiving side for transmitting the optical pulse with the intensity of alpha by the a-base vector by the transmitting side.
Figure BDA0002306423230000038
Figure BDA0002306423230000039
Figure BDA00023064232300000310
Figure BDA00023064232300000311
Figure BDA00023064232300000312
The yield of n photon state measured by a base vector of a transmitting party and a base vector of b of a receiving party is obtained. μ, v, ω represents the average number of photons that the sender uses three different light pulses.
In this embodiment, the sequence of step 3 and step 4 may be exchanged, or may be performed simultaneously.
[ example 2 ] A method for producing a polycarbonate
Step 1: the sender and the receiver of the quantum key distribution system carry out preparation, transmission and measurement of quantum states; however, the quantum state is transmitted and prepared as follows: the sender prepares not less than three quantum states, but the three quantum states are prepared strictly according to the requirements of a simplified BB84 protocol; when measuring the received quantum state, the receiving party measures the quantum state prepared by the transmitting party according to the requirement of the simplified BB84 protocol strictly according to the requirement of the simplified BB84 protocol strictly.
Step 2: the sender and the receiver carry out base vector comparison through an open channel;
and step 3: the data processing module sender and receiver of the quantum key distribution system carry out error correction to obtain the bit error rate measured by the receiver by using the Z basis vector
Figure BDA0002306423230000041
Figure BDA0002306423230000042
Wherein E iszThe bit error rate measured with the Z basis vector for the receiver can be measured directly.
And 4, step 4: the data processing module of the quantum key distribution system calculates the phase error rate measured by the Z basis vector of the receiver
Figure BDA0002306423230000043
Figure BDA0002306423230000044
Wherein, Ya,-(a is 0,1) represents that the sender sends out quantum state | a by adopting Z basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication can be directly measured in real time during actual communication. Y is+,-Represents that the sender sends quantum state | +by adopting X basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication can be directly measured in real time during actual communication.
Wherein, YXXThe quantum state is prepared by the X basis vector for the sender, and the Yield (Yield) obtained by the X basis vector measurement for the receiver can be obtained by calculation or can be directly obtained by real-time measurement during actual communication. Y isZXThe quantum state is prepared by the transmitting party by using the Z basis vector, and the Yield (Yield) measured by the receiving party by using the X basis vector can be obtained by calculation or real-time measurement during communication.
And 5: the data processing module of the quantum key distribution system carries out privacy amplification on the key after discarding the basis vector information to obtain a code rate:
Figure BDA0002306423230000045
wherein f is an error correction coefficient,
Figure BDA0002306423230000046
transmitting by a base vector for a transmitting party and b base vector for a receiving partyThe yield of quantitative light pulses of intensity alpha,
Figure BDA0002306423230000047
the bit error rate measured by the b-base vector is used by the receiving side for transmitting the optical pulse with the intensity of alpha by the a-base vector by the transmitting side.
Figure BDA0002306423230000048
Figure BDA0002306423230000049
Figure BDA00023064232300000410
Figure BDA00023064232300000411
Figure BDA00023064232300000412
The yield of n photon state measured by a base vector of a transmitting party and a base vector of b of a receiving party is obtained. μ, v, ω represents the average number of photons that the sender uses three different light pulses.
In this embodiment, the sequence of step 3 and step 4 may be exchanged, or may be performed simultaneously.
In the method, the bit error rate and the phase error rate are directly determined by actual measurement and can be monitored in real time, and the error rate estimation provided by the method is more compact compared with the existing error rate estimation, so that the bit error rate and the phase error rate of the quantum communication system are improved.
The present application has been described in detail with reference to specific embodiments and illustrative examples, but the description is not intended to limit the application. Those skilled in the art will appreciate that various equivalent substitutions, modifications or improvements may be made to the presently disclosed embodiments and implementations thereof without departing from the spirit and scope of the present disclosure, and these fall within the scope of the present disclosure. The protection scope of this application is subject to the appended claims.

Claims (4)

1. A method for calculating a coding error rate of a quantum key generation system, the method comprising: the method comprises the steps of (1) carrying out,
step 1: the sender and the receiver of the quantum key distribution system carry out preparation, transmission and measurement of quantum states according to a simplified BB84 protocol;
step 2: the sender and the receiver of the quantum key distribution system carry out base vector comparison;
and step 3: the sender and the receiver of the quantum key distribution system carry out error correction to obtain the bit error rate measured by the receiver by using the Z basis vector
Figure FDA0003607786850000011
Figure FDA0003607786850000012
Wherein E isZThe bit error rate measured by the Z basis vector is directly measured in real time during actual communication for a receiver;
and 4, step 4: the data processing module of the quantum key distribution system calculates the phase error rate measured by the Z basis vector of the receiver
Figure FDA0003607786850000013
Figure FDA0003607786850000014
Wherein Y isa,-(a is 0,1) represents that the sender sends out quantum state | a by adopting Z basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication is directly measured in real time during actual communication; y is+,-Indicating sender miningTransmitting quantum state | +with X basis vector>Meanwhile, the receiving party detects the quantum state | ->The yield of the communication is directly measured in real time during actual communication; y isXXPreparing a quantum state for a sender by using the X basis vector, and measuring a lower bound of a yield obtained by a receiver by using the X basis vector, and obtaining the yield through calculation or real-time measurement during communication; y isZXPreparing an upper bound of quantum state for a sender by using the Z basis vector, and measuring the yield obtained by a receiver by using the X basis vector, and obtaining the yield through calculation or real-time measurement during communication;
and 5: the data processing module of the quantum key distribution system performs privacy amplification on the key with the basis vector information discarded to obtain a code rate, which is specifically as follows:
Figure FDA0003607786850000015
wherein f is an error correction coefficient,
Figure FDA0003607786850000016
the yield of the optical pulse with the intensity of alpha is measured by the transmitting side by the a-basis vector and the receiving side by the b-basis vector,
Figure FDA0003607786850000017
the bit error rate is measured by a b-base vector for a transmitting side to transmit an optical pulse with the a-base vector and the intensity of alpha and a receiving side;
Figure FDA0003607786850000018
Figure FDA0003607786850000019
Figure FDA00036077868500000110
Figure FDA00036077868500000111
Figure FDA00036077868500000112
the n photon state yield measured by the transmitting side by the a-base vector and the receiving side by the b-base vector, and mu, v and omega represent the average photon number of three different light pulses adopted by the transmitting side.
2. The computing method according to claim 1, characterized in that: the sender sends pulses of at least three different average photon numbers.
3. The computing method according to claim 1, characterized in that: the quantum state preparation and measurement in step 1 are carried out as follows: the sender prepares not less than three quantum states, but the three quantum states are prepared strictly according to the requirements of a simplified BB84 protocol; when measuring the received quantum state, the receiving party measures the quantum state prepared by the transmitting party according to the requirement of the simplified BB84 protocol strictly according to the requirement of the simplified BB84 protocol strictly.
4. The calculation method according to claim 1, wherein the steps 3 and 4 can be performed in a reversed order or simultaneously.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102185693A (en) * 2011-04-25 2011-09-14 安徽量子通信技术有限公司 Quantum cryptography teaching system based on BB84 protocol and communication method thereof
CN104954122A (en) * 2015-06-18 2015-09-30 清华大学 Quantum key distribution post-processing method and quantum key distribution post-processing system under condition of mixed base vectors
CN108712255A (en) * 2018-06-29 2018-10-26 清华大学 A kind of quantum key distribution system and method

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8122323B2 (en) * 2007-03-08 2012-02-21 Intel Corporation Method, apparatus, and system for dynamic ECC code rate adjustment

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102185693A (en) * 2011-04-25 2011-09-14 安徽量子通信技术有限公司 Quantum cryptography teaching system based on BB84 protocol and communication method thereof
CN104954122A (en) * 2015-06-18 2015-09-30 清华大学 Quantum key distribution post-processing method and quantum key distribution post-processing system under condition of mixed base vectors
CN108712255A (en) * 2018-06-29 2018-10-26 清华大学 A kind of quantum key distribution system and method

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