Calderbank-Shor-Steane码的可靠性与量子密钥分发的安全性
摘要
在Mayers (1996, 2001)给出Bennett-Brassard 1984 (BB84)量子密钥分发协议的安全性证明之后，Shor和Preskill (2000)作出了一个显著观察：BB84协议中隐式地使用了Calderbank-Shor-Steane (CSS)码，并建议其安全性可通过限定所内含的长度为n的CSS码的保真度F(n)来证明，形式为1-F(n) <= exp[-n E+o(n)]，其中E为某正数。本工作给出这样的数E=E(R)作为码率R的函数，以及阈值R'使得当R < R'时E(R)>0，该阈值大于基于本质上由Shor和Preskill (2000)给出的Gilbert-Varshamov界的可达码率。本工作中的码对信道参数的涨落具有鲁棒性，这一事实是严格建立安全性所必需的，且此前文献中对于高于Gilbert-Varshamov码率的情况未曾证明。作为副产品，定量证明了改进型BB84协议针对任意联合（相干）攻击的安全性。
引用
@article{arxiv.quant-ph/0308029,
title = {Reliability of Calderbank-Shor-Steane Codes and Security of Quantum Key Distribution},
author = {Mitsuru Hamada},
journal= {arXiv preprint arXiv:quant-ph/0308029},
year = {2009}
}
备注
No figure. Ver.2: Security criterion slightly refined. 25 pages. Ver.3: Completely revised to fix a serious error. The existence of needed robust codes beyond the Gilbert-Varshamov rate was not proved in the previous versions (or in the literature). Ver.4: Minor errors corrected. Ver.5: Security proof for general joint attacks added. Ver.5: Accepted version; the results and reasonings unchanged; a remark on random sampling added in Appendix C with three references