Non-Asymptotic Bounds via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing
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.
Related
- Binary Quantum Hypothesis Testing with a Rejection Option: The Exact Error-Exponent Trade-off
- Sharp pairwise reduction for quantum hypothesis testing
- Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination
- Hypothesis-awkward: Property-Based Testing Strategies for Awkward Array
- Testing the Kerr hypothesis with orbital frequencies: lessons from spacelike singularities and black bounces
BibTeX
@misc{lizarribarcarrillo2026nonasymptotic,
title = {{Non-Asymptotic Bounds via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing}},
author = {Jorge Lizarribar-Carrillo and Gonzalo Vazquez-Vilar and Tobias Koch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39784},
eprint = {2610.39784},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39784},
}
RIS
TY - UNPB
TI - Non-Asymptotic Bounds via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing
AU - Jorge Lizarribar-Carrillo
AU - Gonzalo Vazquez-Vilar
AU - Tobias Koch
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39784
UR - https://arxiv.org/abs/2610.39784
AB - 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.
ER -