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arXiv · 2610.39784

Non-Asymptotic Bounds via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing

Jorge Lizarribar-Carrillo·Gonzalo Vazquez-Vilar·Tobias Koch
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Abstract

Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces novel lower and upper bounds for asymmetric quantum hypothesis testing based on the Nussbaum-Szkoła mapping. Together, these bounds provide a unified recovery of both converse and achievability results across all major asymptotic regimes, including large-, moderate-, and small-deviations. Unlike existing bounds, which either rely on technically involved information-spectrum arguments or suffer from fixed prefactors and limited applicability in the non-asymptotic regime, the proposed bounds arise from a unified framework and enable, in some cases, the direct use of classical results. It is further demonstrated that these bounds provide accurate approximations to the optimal quantum error trade-off function at small blocklengths. Numerical comparisons with existing bounds, including those based on fidelity and information spectrum methods, highlight their improved tightness.

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Jorge Lizarribar-Carrillo, Gonzalo Vazquez-Vilar, Tobias Koch. 2026-10-29. Non-Asymptotic Bounds via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing. https://arxiv.org/abs/2610.39784

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