A Converse Bound via the Nussbaum-Szko{\l}a Mapping for Quantum Hypothesis Testing
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-Szko{\l}a 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.
Cite
@article{arxiv.2601.13970,
title = {A Converse Bound via the Nussbaum-Szko{\l}a Mapping for Quantum Hypothesis Testing},
author = {Jorge Lizarribar-Carrillo and Gonzalo Vazquez-Vilar and Tobias Koch},
journal= {arXiv preprint arXiv:2601.13970},
year = {2026}
}