有限长度量子密钥的纠错误码率估计仿真分析

基于奇偶检错-汉明纠错算法的误码率后验分布参数，用仿真数据直接估计纠错后的误码率及其置信区间。实验利用了两个伪随机二进制序列替代原始量子密钥，长度为1.4×10-7，误码呈二项分布，通过奇偶检错后利用(7,4)汉明码对奇偶性不一致的码字进行纠错。实验结果表明：当初始误码率为3%时，通过一次检错、纠错，误码率降至2.47×10-3，置信度为95%的上限值为2.77×10-3；当初始误码率为0.1%时，通过一次纠错，误码率降至1.43×10-7，置信度为95%的上限值为10.54×10-7。该方法有效地估计了奇偶-汉明纠错码对有限长度原始量子密钥纠错后的误码率，为量子密钥分配后续处理提供了可靠的数据支持。

Estimates for BER of error correcting on finite quantum key

Based on the parameters of posterior distribution of BER (Bit Error Rate) regarding parity check-Hamming correction protocol,the BER and its confidence interval of the remaining quantum keys are directly estimated. In experiment,instead of the raw quantum keys,we use two pseudo-random binary sequences which have the length of 1.4×10-7 and the BER follow binomial distribution.The Error correction process utilizes the parity code and Hamming code for error detection and correction respectively.The experimental results showed that: when the initial bit error rate at 3% and 0.1%,by one time error detection and error correction, the BER falls to 2.47×10-3 and 1.43×10-7 respectively, when the confidence at 95%, the corresponding upper limit of BER at 2.77×10-3 and 10.57×10-7 respectively. These experimental results effectively assessed parity - Hamming error correction performance on the finite quantum keys,and provided reliable data for the post-processing in the quantum key distribution.