Understand
A variety of new measures of quantum Renyi mutual information and quantum Renyi conditional entropy have recently been proposed, and some of their mathematical properties explored.
- Here, we show that the Renyi mutual information attains operational meaning in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state and the alternate 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 Renyi conditional entropy by choosing an alternative hypothesis that consists of product states that are maximally mixed on one system.