A Converse Bound via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing

• URL: http://arxiv.org/abs/2601.13970v1
• Date: Tue, 20 Jan 2026 13:48:28 GMT
• Title: A Converse Bound via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing
• Authors: Jorge Lizarribar-Carrillo, Gonzalo Vazquez-Vilar, Tobias Koch,
• Abstract summary: This paper introduces a novel lower bound for asymmetric quantum hypothesis testing based on the Nussbaum-Szkoa mapping.<n>The proposed bound arises from a single expression and enables, in some cases, the direct use of classical results.
• Score: 3.1351527202068445
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szkoła mapping. The lower bound provides a unified recovery of converse 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 bound arises from a single expression and enables, in some cases, the direct use of classical results. It is further demonstrated that the proposed bound provides 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 its improved tightness and practical relevance.

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