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arXiv · 2403.13584

On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding

Hao-Chung Cheng·Li Gao
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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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Hao-Chung Cheng, Li Gao. 2024-03-20. On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding. https://arxiv.org/abs/2403.13584

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