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Chain rule for quantum relative entropies and their applications in quantum information theory

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The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on the individual systems. In this talk, we will discuss similar chain rules for two different quantum relative entropies, that is, the Umegaki relative entropy and the Belavkin-Staszewski (BS) relative entropy. These new chain rules admit important applications in the context of asymptotic quantum channel discrimination and quantum channel capacities. More precisely, the chain rule for the Umegaki relative entropy allows us to solve an open problem in quantum channel discrimination that adaptive protocols cannot improve the error rate for asymmetric channel discrimination compared to non-adaptive strategies. The chain rule for the BS relative entropy helps to sharpen single-letter converse bounds on quantum channel capacities in a significant way.

This talk is based on arXiv papers: 1909.05826 and 1909.05758.

This talk is part of the CQIF Seminar series.

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