Derives single-letter Stein exponent for distributed quantum binary hypothesis testing under zero-rate communication when the alternative state is a product of marginals, with multi-letter expressions for the general case.
Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb
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abstract
We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large numbers only. Joint convexity of the quantum relative entropy is proven too, resulting in a self-contained elementary version of Tropp's approach to Lieb's concavity theorem, according to which the map tr(exp(h+log a)) is concave in a on positive operators for self-adjoint h.
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quant-ph 1years
2024 1verdicts
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Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints
Derives single-letter Stein exponent for distributed quantum binary hypothesis testing under zero-rate communication when the alternative state is a product of marginals, with multi-letter expressions for the general case.