On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding
arxiv(2024)
摘要
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 Rényi divergences [Lett. Math. Phys, 107(12), 2017].
Then, we show that the variational expression is a direct consequence of
Hölder's inequality.
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