Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
The Converse Part of The Theorem for Quantum Hoeffding Bound
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abstract
We prove the converse part of the theorem for quantum Hoeffding bound on the asymptotics of quantum hypothesis testing, essentially based on an argument developed by Nussbaum and Szkola in proving the converse part of the quantum Chernoff bound. Our result complements Hayashi's proof of the direct (achievability) part of the theorem, so that the quantum Hoeffding bound has now been established.
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UNVERDICTED 4representative citing papers
The reverse sandwiched Renyi divergence for alpha in (0,1) exactly equals the optimal Hoeffding exponent for discriminating a thermal equilibrium state from a probe with unknown dephasing in the energy basis.
For composite quantum hypothesis testing with a mixed IID null hypothesis, the optimal type-II error exponent is the worst-case component when type-I error vanishes, but not for fixed nonzero type-I error.
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).
citing papers explorer
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Doubly minimized Petz and sandwiched Renyi mutual information: Properties
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
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Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing
The reverse sandwiched Renyi divergence for alpha in (0,1) exactly equals the optimal Hoeffding exponent for discriminating a thermal equilibrium state from a probe with unknown dephasing in the energy basis.
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Generalized quantum Stein's lemma for mixed sources
For composite quantum hypothesis testing with a mixed IID null hypothesis, the optimal type-II error exponent is the worst-case component when type-I error vanishes, but not for fixed nonzero type-I error.
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Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).