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On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding
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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.
Forward citations
Cited by 2 Pith papers
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Probabilistic Entanglement Distillation: Error Exponents via Postselected Quantum Hypothesis Testing Against Separable States
Probabilistic entanglement distillation under approximate (dually) non-entangling instruments has error exponent equal to the regularized Hilbert projective metric to separable states.
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Strong converse rate for asymptotic hypothesis testing in type III
In any von Neumann algebra, the strong converse rate B_r(ρ∥η) equals the Hoeffding anti-divergence H*_r(ρ∥η) when aρ ≤ η.
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