Correlation detection and an operational interpretation of the R�nyi mutual information

Publication Type:
Journal Article
Journal of Mathematical Physics, 2016, 57 (10)
Issue Date:
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A variety of new measures of quantum R�nyi mutual information and quantum R�nyi conditional entropy have recently been proposed, and some of their mathematical properties explored. Here, we show that the R�nyi mutual information attains operational meaning in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state and the alternative hypothesis consists of all product states that share one marginal with the null hypothesis. This hypothesis testing problem occurs naturally in channel coding, where it corresponds to testing whether a state is the output of a given quantum channel or of a "useless" channel whose output is decoupled from the environment. Similarly, we establish an operational interpretation of R�nyi conditional entropy by choosing an alternative hypothesis that consists of product states that are maximally mixed on one system. Specialized to classical probability distributions, our results also establish an operational interpretation of R�nyi mutual information and R�nyi conditional entropy.
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