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Strong converse rate for asymptotic hypothesis testing in type III

Strong converse rate for asymptotic hypothesis testing in type III

来源:Arxiv_logoArxiv
英文摘要

We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative Rényi entropy in the strong converse of hypothesis testing. The specific task is to distinguish between two quantum states given many copies. We use a reduction method of Haagerup, Junge, and Xu (2010) to approximate relative entropy inequalities in an arbitrary von Neumann algebra by those in finite von Neumann algebras. Within these finite von Neumann algebras, it is possible to approximate densities via finite spectrum operators, after which the quantum method of types reduces them to effectively commuting subalgebras. Generalizing beyond the hyperfinite setting shows that the operational meaning of sandwiched Rényi entropy is not restricted to the matrices but is a more fundamental property of quantum information. Furthermore, applicability in general von Neumann algebras opens potential new connections to random matrix theory and the quantum information theory of fundamental physics.

Nicholas Laracuente、Marius Junge

物理学计算技术、计算机技术

Nicholas Laracuente,Marius Junge.Strong converse rate for asymptotic hypothesis testing in type III[EB/OL].(2025-07-10)[2025-07-20].https://arxiv.org/abs/2507.07989.点此复制

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