The semiring of dichotomies and asymptotic relative submajorization

Perry, Christopher and Vrana, Péter and Werner, Albert H. (2021) The semiring of dichotomies and asymptotic relative submajorization. IEEE TRANSACTIONS ON INFORMATION THEORY. ISSN 0018-9448 (In Press)

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Abstract

We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichotomies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Rényi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing.

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