ISSN 1000-1239 CN 11-1777/TP

计算机研究与发展 ›› 2021, Vol. 58 ›› Issue (9): 1906-1914.doi: 10.7544/issn1000-1239.2021.20210346

所属专题: 2021量子计算专题

• 基础理论 • 上一篇    下一篇

量子假设检验互信息

张淑仪,席政军   

  1. (陕西师范大学计算机科学学院 西安 710062) (zsy18@snnu.edu.cn)
  • 出版日期: 2021-09-01
  • 基金资助: 
    国家自然科学基金项目(61671280);中央高校基本科研业务费专项资金(GK201902007);陕西师范大学优秀学术青年骨干项目(16QNGG013)

Quantum Hypothesis Testing Mutual Information

Zhang Shuyi Xi Zhengjun   

  1. (College of Computer Science, Shaanxi Normal University, Xi’an 710062)
  • Online: 2021-09-01
  • Supported by: 
    This work was supported by the National Natural Science Foundation of China (61671280), the Fundamental Research Funds for the Central Universities (GK201902007), and the Funded Projects for the Academic Leaders and Academic Backbones, Shaanxi Normal University (16QNGG013).

摘要: von Neumann互信息是Shannon互信息在量子信息中的推广,在量子信道容量中有非常好的应用.由于量子态的非对易性,许多经典信息论中的量化在量子信息中有完全不等价的推广定义.量子假设检验相对熵来自于假设检验问题,是量子信息处理中常用的基本量化之一.使用量子假设检验相对熵讨论量子互信息. 首先讨论量子假设检验相对熵的一些基本性质,并给出该量化和其他量子广义熵之间的关系. 然后结合相对熵的性质,给出量子假设检验互信息的定义,并讨论其性质,比如:数据处理不等式.通过互信息与条件熵之和重点讨论互信息的链式法则.

关键词: 量子假设检验, 相对熵, 互信息, 条件熵, 链式法则

Abstract: von Neumann mutual information is a generalization of Shannon mutual information in quantum information theory, and it has been found to have useful applications in the channel capacity. The many classical quantifiers can be extended for pairs of quantum states in various inequivalent ways, due to the non-commutativity of quantum states. Quantum hypothesis testing relative entropy comes from the hypothesis testing question, and it is one of the most fundamental primitives in quantum information processing. We discuss the quantum mutual information with respect to quantum hypothesis testing relative entropy. We give some properties of quantum hypothesis testing relative entropy, and give the relationships between it and other quantum generalized entropies. Using relative entropy, we define quantum hypothesis testing mutual information, and exhibit some properties, such as, data processing inequality. Using the sum between mutual information and condition entropy, we discuss the chain rules, which are generally an important technical tool in information theory.

Key words: quantum hypothesis testing, relative entropy, mutual information, conditional entropy, chain rules

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