On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding

• URL: http://arxiv.org/abs/2403.13584v1
• Date: Wed, 20 Mar 2024 13:34:23 GMT
• Title: On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding
• Authors: Hao-Chung Cheng, Li Gao,
• Abstract summary: Strong converse theorems refer to the study of impossibility results in information theory. Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing. We show that the variational expression of measured R'enyi divergences is a direct consequence of H"older's inequality.
• Score: 16.207627554776916
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which servers as a primitive tool for establishing a variety of tight strong converse theorems in quantum information theory. In this short note, we demonstrate an alternative one-line proof for this bound via the variational expression of measured R\'enyi divergences [Lett. Math. Phys, 107(12), 2017]. Then, we show that the variational expression is a direct consequence of H\"older's inequality.

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