ISSN 1000-1239 CN 11-1777/TP

Journal of Computer Research and Development ›› 2021, Vol. 58 ›› Issue (9): 1906-1914.doi: 10.7544/issn1000-1239.2021.20210346

Special Issue: 2021量子计算专题

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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).

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

CLC Number: