The semiring of dichotomies and asymptotic relative submajorization

• URL: http://arxiv.org/abs/2004.10587v1
• Date: Wed, 22 Apr 2020 14:13:26 GMT
• Title: The semiring of dichotomies and asymptotic relative submajorization
• Authors: Christopher Perry, P\'eter Vrana, Albert H. Werner
• Abstract summary: 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 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 R\'enyi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing.

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