Smith Graeme, Renes Joseph M, Smolin John A
Institute for Quantum Information, California Institute of Technology 107-81, Pasadena, California 91125, USA.
Phys Rev Lett. 2008 May 2;100(17):170502. doi: 10.1103/PhysRevLett.100.170502. Epub 2008 Apr 28.
A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates under various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by a single-letter formula involving optimization over a single use of an effective channel. We explore the possibility of such a formula for the simplest and most widely used QKD protocol, Bennnett-Brassard-84 with one-way classical postprocessing. We show that a conjectured single-letter formula is false, uncovering a deep ignorance about good private codes and exposing unfortunate complications in the theory of QKD. These complications are not without benefit-with added complexity comes better key rates than previously thought possible. The threshold for secure key generation improves from a bit error rate of 0.124 to 0.129.
信息论和密码学的一个核心目标是在各种限制和安全要求下找到最优通信速率的简单特征描述。理想情况下，量子密钥分发（QKD）协议的最优密钥率应由一个单字母公式给出，该公式涉及对有效信道单次使用的优化。我们探讨了对于最简单且使用最广泛的QKD协议——具有单向经典后处理的Bennett-Brassard-84协议——存在这样一个公式的可能性。我们证明了一个推测的单字母公式是错误的，揭示了对良好私有码的深刻无知，并暴露了QKD理论中令人遗憾的复杂性。这些复杂性并非没有益处——随着复杂性的增加，密钥率比之前认为可能的要好。安全密钥生成的阈值从误码率0.124提高到了0.129。
