CN112929080A - 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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CN112929080A
CN112929080A CN201911242725.0A CN201911242725A CN112929080A CN 112929080 A CN112929080 A CN 112929080A CN 201911242725 A CN201911242725 A CN 201911242725A CN 112929080 A CN112929080 A CN 112929080A
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/07—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
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    • H04B10/07953—Monitoring or measuring OSNR, BER or Q
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    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • 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
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Abstract

The method is used for calculating the code forming error rate of a four-transmission three-reception three-state protocol, and therefore a better code forming rate estimation is obtained, the method does not need to depend on a basic detection efficiency condition, the estimated value of the phase error rate is more compact, and the calculation mode is simpler. The method mainly comprises the following steps: step 1: a sender and a receiver of quantum key distribution carry out preparation and measurement of quantum states according to a four-sending three-receiving three-state 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.
In order to simplify the complexity of the experimental setup of the quantum key distribution system, researchers have proposed a three-state protocol (this three-state protocol requires three different quantum states to be prepared at the sender and four different quantum states to be tested at the receiver, c. -h.f. funging and h. -k.lo, phys. rev.a 74,042342 (2006)), which in 2006 has completed the proof of unconditional safety, but has not been practical due to the fact that this scheme has an excessively high estimation of the phase error rate of single photons.
Since then, further theoretical studies in 2014 (k.tamaki, m.curty, g.kato, h. — k.lo, and k.azuma, phys.rev.a 90,052314(2014)) show that the tri-state protocol is loss tolerant, which means that it is suitable for long-range quantum key distribution even in the case of non-ideal light sources. More importantly, the research realizes that the safe code rate of the tri-state protocol is improved to the same level as the standard BB84 protocol under the condition of asymptotic limit, so that the tri-state protocol has practicability.
A four-transmission three-reception tri-state protocol: the basis vector was prepared and measured as follows: a sender (Alice) for 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, the probability of selecting the X basis vector is 1-p, when the Z basis vector is selected, Alice randomly prepares a quantum state |0> and a quantum state |1>, the probability of preparing the quantum state |0> is p/2, the probability of preparing the quantum state |1> is p/2, when the X basis vector is selected, Alice randomly prepares a quantum state | + > and a quantum state | - >, the probability of preparing the quantum state | + | > is (1-p)/2, and the probability of preparing the quantum state | - > is (1-p)/2. A receiving party (Bob) of quantum key distribution randomly selects a Z basis vector and an X basis vector to measure the 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 Bob selects the Z basis vector, measuring |0>, |1 >; when Bob selects the X basis vector, measure | + >. Above 0< p, q < 1.
However, the four-transmission three-reception tri-state protocol needs to satisfy a detection efficiency condition independent of the measurement basis vector, and the condition is difficult to satisfy in a part of 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 secure code rate calculation method of the tri-state protocol is provided, the method does not need to depend on the basic detection efficiency condition, the estimated value of the phase error rate is more compact, and the calculation method is simpler.
Step 1: a sender and a receiver of quantum key distribution respectively carry out preparation and measurement of quantum states according to a four-sending three-receiving three-state protocol;
preferably, the quantum state preparation and measurement method in step 1 may adopt a method adopted in a protocol not less than four states, but during subsequent use, the quantum state preparation and measurement is selected according to a method described in a four-transmission three-reception three-state protocol.
Step 2: comparing the basis vectors of the sender and the receiver;
and step 3: the error correction is carried out by the sender and the receiver to obtain the bit error rate measured by the Z basis vector of the receiver
Figure BDA0002306710810000021
Figure BDA0002306710810000022
Wherein E iszThe bit error rate measured with the Z basis vector for the receiver can be directly derived from the actual measurement.
And 4, step 4: calculating the phase error rate of the Z basis vector measurement at the receiver
Figure BDA0002306710810000023
The tri-state protocol of four-transmitting and three-receiving adopts the following formula:
Figure BDA0002306710810000024
wherein, Y-,+Preparation of quantum state | ->Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication. Y is+,+Quantum state | +prepared by using X basis vector for sender>Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication. EXThe bit error rate measured with the X basis vector for the receiver can be directly obtained from the actual measurement.
And 5: and carrying out privacy amplification on the key after discarding the basis vector information to obtain the resultant code rate.
Figure BDA0002306710810000025
Wherein f is an error correction coefficient,
Figure BDA0002306710810000026
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 BDA0002306710810000027
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 BDA0002306710810000028
Figure BDA0002306710810000029
Figure BDA00023067108100000210
Figure BDA00023067108100000211
Figure BDA00023067108100000212
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.
Wherein, the step 3 and the step 4 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: a sender and a receiver of quantum key distribution respectively carry out preparation and measurement of quantum states according to a four-sending three-receiving three-state protocol;
step 2: the sender and the receiver carry out base vector comparison through an open channel;
and step 3: the error correction is carried out by the sender and the receiver to obtain the bit error rate measured by the Z basis vector of the receiver
Figure BDA0002306710810000031
Figure BDA0002306710810000032
Wherein E iszThe bit error rate measured with the Z basis vector for the receiver can be directly derived from the actual measurement.
And 4, step 4: calculating the phase error rate of the Z basis vector measurement at the receiver
Figure BDA0002306710810000033
Figure BDA0002306710810000034
Wherein, Y-,+Preparation of quantum state | ->Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication. Y is+,+Quantum state | +prepared by using X basis vector for sender>Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication. EXThe bit error rate measured with the X basis vector for the receiver can be directly obtained from the actual measurement.
And 5: and carrying out privacy amplification on the key after discarding the basis vector information to obtain the resultant code rate.
Figure BDA0002306710810000035
Wherein f is an error correction coefficient,
Figure BDA0002306710810000036
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 BDA0002306710810000037
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 BDA0002306710810000038
Figure BDA0002306710810000039
Figure BDA00023067108100000310
Figure BDA00023067108100000311
Figure BDA00023067108100000312
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 ]
Step 1: a sender of quantum key distribution carries out quantum state preparation according to a communication protocol of not less than four quantum states, wherein the four quantum states are strictly prepared according to a four-sending three-receiving three-state protocol. The receiving party measures each quantum state sent by the sending party according to a four-sending three-receiving three-state protocol, wherein the four quantum states prepared by the sending party according to the four-sending three-receiving three-state protocol are strictly measured according to the four-sending three-receiving three-state protocol;
step 2: the sender and the receiver carry out base vector comparison through an open channel;
and step 3: the error correction is carried out by the sender and the receiver to obtain the bit error rate measured by the Z basis vector of the receiver
Figure BDA0002306710810000041
Figure BDA0002306710810000042
Wherein E iszThe bit error rate measured with the Z basis vector for the receiver can be directly derived from the actual measurement.
And 4, step 4: calculating the phase error rate of the Z basis vector measurement at the receiver
Figure BDA0002306710810000043
Figure BDA0002306710810000044
Wherein, Y-,+Preparation of quantum state | ->Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication. Y is+,+Quantum state | +prepared by using X basis vector for sender>Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication. EXThe bit error rate measured with the X basis vector for the receiver can be directly obtained from the actual measurement.
And 5: and carrying out privacy amplification on the key after discarding the basis vector information to obtain the resultant code rate.
Figure BDA0002306710810000045
Wherein f is an error correction coefficient,
Figure BDA0002306710810000046
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 BDA0002306710810000047
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 BDA0002306710810000048
Figure BDA0002306710810000049
Figure BDA00023067108100000410
Figure BDA00023067108100000411
Figure BDA00023067108100000412
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.
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 (9)

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: a sender and a receiver of quantum key distribution respectively carry out preparation and measurement of quantum states according to a four-sending three-receiving three-state protocol;
step 2: comparing the basis vectors of the sender and the receiver;
and step 3: the error correction is carried out by the sender and the receiver to obtain the bit error rate measured by the Z basis vector of the receiver
Figure FDA0002306710800000011
Figure FDA0002306710800000012
And 4, step 4: calculating the phase error rate of the Z basis vector measurement at the receiver
Figure FDA0002306710800000013
Figure FDA0002306710800000014
And 5: and carrying out privacy amplification on the key after discarding the basis vector information to obtain the resultant code rate.
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 method of claim 1, wherein the preparing of the quantum states comprises a sender sending pulses of no less than four quantum states, but wherein the preparing of the four quantum states is prepared in a manner described in a four-send-three-receive tri-state protocol.
4. The computing method of claim 1, wherein the measuring of the quantum states comprises measuring at least three of the quantum states by a receiving party, and the three quantum states are three of four quantum states prepared by a sending party according to a four-sending three-receiving three-state protocol; and when the receiver is in three quantum states, the receiver performs measurement in a manner described by a four-transmission three-receiving three-state protocol.
5. The computing method according to claim 1, wherein E in step 3ZThe bit error rate measured by the Z basis vector for the receiving side can be measured in real time during communication.
6. The computing method according to claim 1, wherein E in step 4XThe bit error rate measured by the X-base vector for the receiving side can be measured in real time during communication.
7. The method of claim 1, wherein Y in step 4 is-,+Preparation of quantum state | ->Meanwhile, the receiver measures the quantum state | +with the X basis vector>The obtained yield can be measured in real time during communication.
8. The method of claim 1, wherein Y in step 4 is+,+Quantum state | +prepared by using X basis vector for sender>Meanwhile, the receiver measures the quantum state | +with the X basis vector>ObtainedThe yield can be measured in real time during communication.
9. 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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* Cited by examiner, † Cited by third party
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CN117118614A (en) * 2023-10-23 2023-11-24 浙江九州量子信息技术股份有限公司 Phase drift and phase error online correction method of phase coding QKD system

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CN105049200A (en) * 2015-08-14 2015-11-11 清华大学 Data post-processing method of quantum key distribution system
CN105553648A (en) * 2014-10-30 2016-05-04 阿里巴巴集团控股有限公司 Quantum key distribution, privacy amplification and data transmission methods, apparatuses, and system

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CN105553648A (en) * 2014-10-30 2016-05-04 阿里巴巴集团控股有限公司 Quantum key distribution, privacy amplification and data transmission methods, apparatuses, and system
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CN117118614B (en) * 2023-10-23 2024-01-23 浙江九州量子信息技术股份有限公司 Phase drift and phase error online correction method of phase coding QKD system

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