In a composite quantum hypothesis testing scenario with dephasing, the reverse sandwiched Renyi divergence for alpha in (0,1) exactly determines the single-copy Hoeffding exponent.
The Converse Part of The Theorem for Quantum Hoeffding Bound
5 Pith papers cite this work, alongside 75 external citations. Polarity classification is still indexing.
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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 5representative citing papers
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.
Explicit formulas are given for regularized Rényi divergences of several kinds between fermionic quasifree states, with all types coinciding in the single-mode case and remaining distinct for multiple modes per site.
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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Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing
In a composite quantum hypothesis testing scenario with dephasing, the reverse sandwiched Renyi divergence for alpha in (0,1) exactly determines the single-copy Hoeffding exponent.
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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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R\'enyi divergences and binary state discrimination error exponents for fermionic quasi-free states
Explicit formulas are given for regularized Rényi divergences of several kinds between fermionic quasifree states, with all types coinciding in the single-mode case and remaining distinct for multiple modes per site.
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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).