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Computer Engineering and Applications Journal

Research on application of quantum LDPC code for BB84 quantum key distribution

Shengmei Zhao

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Considering noise in the quantum channel of BB84 quantum key distribution protocol,an improved model of BB84 protocol with quantum error correction code,such as Quantum Low Density Parity Check code(QLDPC) is proposed in this paper.By numerical simulation,the effect of quantum error correction code on BB84 protocol is analyzed in the case of the efficiency of transmission rate.The results show that quantum LDPC codes have good ability to overcome the noise,raise the efficiency of transmission rate and verify the availability of the improved model.

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Considering noise in the quantum channel of BB84 quantum key distribution protocol,an improved model of BB84 protocol with quantum error correction code,such as Quantum Low Density Parity Check code(QLDPC) is proposed in this paper.By numerical simulation,the effect of quantum error correction code on BB84 protocol is analyzed in the case of the efficiency of transmission rate.The results show that quantum LDPC codes have good ability to overcome the noise,raise the efficiency of transmission rate and verify the availability of the improved model.
Quantum encryption guarantees the absolute security of key distribution from the physical mechanism. However, in the process of quantum key distribution (QKD), quantum channel noise will reduce the transmission efficiency. Quantum low-density parity check (quantum LDPC) code has become a hot research topic of quantum error correcting code due to its great flexibility in the choice of code length and code rate and its dependence on sparse graphs. In order to improve the transmission reliability, a QKD protocol based on BB84 and quantum LDPC code is designed. First, we construct a quantum LDCP error correcting code. Then we utilize the error correcting code and BB84 to construct our QKD protocol. Finally, we analyze the influence of the quantum LDPC code on the proposed protocol. The results show that the key transmission efficiency of the our protocol is improved, and the validity of the QKD protocol based on BB84 and quantum LDPC codes in noisy quantum channels is verified.
In this paper,the security of BB84 key distribution protocol is considered.We assume that in the protocol the eavesdropper Eve intercepts/resends photons transmitted between Alice and Bob with probability e.First,the BB84 key distribution protocol will be made equivalent to a special Wire-tap channel model,where the main channel is a binary symmetric channel with probability of flipping bits 0.25e and the eavesdropper's channel is a binary erasure channel with probability of erasure 1-e.Using the coding method and properties of quantum LDPC codes CSS(C1,C2) for secure communication across the Wire-tap channel in the BB84 protocol is an equivalent proof of the security of BB84 protocol.Finally,the tolerable error rate of the BB84 protocol based on quantum LDPC codes can be obtained by calculating the secrecy capacity of this special Wire-tap channel.
In order to solve the low key distribution efficiency problem of the BB84 protocol, an improved BB84 quantum key distribution scheme is presented in this paper. Firstly the same polarization basis is used by the sender and the receiver with the consistent agreement. This process could make quantum key distribution rate higher. Then signature combined with the error correction method based on the odd and even parity is used to ensure the safety of the transmission. The analyses results indicate that the advantage of the improved scheme lies in that the all photons sent to Bob by Alice are useful. It can not only reduce the time extracting the original key, but also solve the authentication problem in the process of communication. The key distribution efficiency is two times of the original BB84 protocol improved scheme.
In the quantum key distribution (QKD) process, the presence of noise in the quantum channel reduces the efficiency of QKD with low transmission reliability. Quantum error correcting codes (QECCs) can weaken the impact of noise on the final result due to its flexibility in code length and rate selection. In this paper, QECCs is used to overcome the adverse effects of quantum channel noise, and a QKD protocol based on quantum CSS error correcting codes is proposed. Firstly, we construct the corresponding quantum CSS codes based on classical linear code, then modify and simplify some steps of BB84 protocol by using the characteristics of error correcting codes to design the new protocol. Through theoretical deduction, our QKD protocol based on quantum CSS codes improves the security of key transmission, and the confidentiality of transmission in the noisy quantum channel is also enhanced.
In this paper, a construction method of quantum low density parity check codes (quantum LDPC) which based on classical quasi-cyclic sparse sequence is proposed, and the quantum code QLDPC(3,8)(16,6) and QLDPC(3,8)(64,24) are selected as examples to illustrate this construction method. The performances of this kind quantum LDPC codes are discussed over the bit-flipping channel by numerical simulations. The results show that these quantum codes have good ability to correct error in quantum channel.
This article will BB84 key distribution protocol seen as a Wire-tap channel model, the main channel is a binary symmetric channel, bit flipping rate 0.25e, Wire-tap channel is a binary erasure channel, deleted probability 1-e, through quantum LDPC coding way, in the BB84 write about the main channel to achieve secure communication, while the security of the BB84 protocol proof. Finally, the Wire-tap channel capacity of safety is calculated, and ultimately get the BB84 protocol of quantum LDPC codes under the tolerable error rate.