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ACM Turing Celebration Conference - China (ACM TURC)

A quantum key distribution protocol based on LDPC error correcting codes

Wei Jia, Ying Zhang, Hao Cheng Yu, Yuxiang Bian

Published May 17, 2019• 3 citations
Publisher

Abstract

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.

DOI
10.1145/3321408.3326652

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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.
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.
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.
For the post-processing of the quantum-key-distribution (QKD) system, the error correction is the most important step, whose efficiency significantly influences the final key generation rate. Traditionally, the error-correction algorithm is developed based on the binary symmetrical channel model. However, this may not comply with the actual channel status. For example, for the fiber-based QKD system, differentiable statuses of the fiber (unstable or steady) should exist for some time and cause different bit error rates. If this channel feature can be exploited, it may considerably improve the error-correction efficiency. This paper proposes to introduce the Gilbert-Elliott (GE) model to analyze the QKD channel. The error-correction algorithm adopts the low-density parity-check (LDPC) code. The GE nodes are added into the traditional belief propagation (BP) algorithm of the LDPC decoder. Simulation results showed that the remaining frame error rate could be improved from ${10}^{\ensuremath{-}2}$ (or ${10}^{\ensuremath{-}3}$) to ${10}^{\ensuremath{-}4}$. An actual QKD system with the quantum channel state under manual control was adopted to collect the key bit string. By analyzing the occurrence probability of the kkk consecutive "1," the key bit string showed closely matched distribution with the GE model prediction. After the error correction, the remaining bit error rate of the modified BP algorithm was significantly smaller than that of the standard BP algorithm with an improvement of more than 2 orders of magnitude. Both simulation and actual experimental results demonstrate that our proposed method can greatly improve the error-correction efficiency if the channel characteristic of the QKD system is accurately exploited, which provides an efficient way to generate a higher key rate.
In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed computational complexity of mathematical problems. BB84 protocol performances can be reduced by various errors and information leakages such as limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping. The proposed reconciliation method allowed to weed out these errors by using Turbo codes. Since their high error correction capability implies getting low errors, this method has high performance especially when compared to the last method presented in the literature based on Low-Density Parity Check codes (LDPC). In particular, we demonstrate that our method leads to a significant improvement of the protocol security and of the Bit Error Rate (BER) even with great eavesdropping capability.
In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed computational complexity of mathematical problems. BB84 protocol performances can be reduced by various errors and information leakages such as limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping. The proposed reconciliation method allowed to weed out these errors by using Turbo codes. Since their high error correction capability implies getting low errors, this method has high performance especially when compared to the last method presented in the literature based on Low- Density Parity Check codes (LDPC). In particular, we demonstrate that our method leads to a significant improvement of the protocol security and of the Bit Error Rate (BER) even with great eavesdropping capability.
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.