Cryptographic distinguishability measures for quantum-mechanical states
Cryptographic distinguishability measures for quantum-mechanical states
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DOI：
10.1109/18.761271
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发表时间：
1999-05-01
影响因子：
2.5
通讯作者：
van de Graaf, J
中科院分区：
文献类型：
--
作者：
Fuchs, CA;van de Graaf, J
本文主要是说明性的，调查了量子力学状态可区分性的四种度量。这是从密码学家的角度完成的，特别关注量子密码学的应用。所考虑的每个度量都植根于概率分布可区分性的类似经典度量：即识别错误的概率、柯尔莫哥洛夫距离、Bhattachargya 系数和香农可区分性（通过互信息定义）。这些度量在统计模式识别和经典密码学中有着悠久的使用历史。我们获得了几个将量子可区分性度量相互关联的不等式，其中之一对于证明量子加密密钥分发的安全性可能至关重要。另一方面，这些度量及其连接不等式用于定义两个量子态族的密码指数不可区分性的单一概念。这是一个可能在分析各种量子密码协议时有用的工具。
This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattachargya coefficient, and the Shannon distinguishability (as defined through mutual information), These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states, This is a tool that may prove useful in the analysis of various quantum-cryptographic protocols.