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This research resolves a long-standing conjecture by establishing dimension-free one-shot bounds for multiple quantum state discrimination, effectively removing previous dimension-dependent limitations. By proving the achievability of the multiple quantum Chernoff distance in infinite-dimensional spaces, the work provides sharp asymptotics for optimal error probabilities in quantum hypothesis testing. These theoretical advances refine the fundamental limits of distinguishing quantum states, offering tighter performance guarantees for quantum information protocols.
Multiple Quantum Hypothesis Testing: One-Shot Pairwise Bounds and Sharp Asymptotics
arXiv:2606.06246v1 Announce Type: new Abstract: We consider Bayesian discrimination among multiple quantum states and establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors. This resolves a conjecture of Audenaert and Mosonyi [J. Math. Phys. 55 (2014)] and improves the multiple quantum Chernoff bound of Li [Ann. Statist. 44 (2016)] by removing its dimension-dependent prefactor. In the asymptotic many-copy regime, our bound proves the achievability of the multiple quantum Chernoff distance for arbitrary separable Hilbert spaces, thereby settling the previously open infinite-dimensional case, and further yields constant-factor sharp asymptotics for the optimal error probability. In binary quantum hypothesis testing, we prove that the minimum error probability is characterized, up to universal constants, by a trace harmonic-mean quantity. Consequently, the optimal binary quantum error probability is within a factor of two of the optimal classical error probability for the associated Nussbaum-Szko{\l}a distributions, complementing the lower bound of Nussbaum and Szko{\l}a [Ann. Statist. 37 (2009)].
Abstract:We consider Bayesian discrimination among multiple quantum states and establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors. This resolves a conjecture of Audenaert and Mosonyi [J. Math. Phys. 55 (2014)] and improves the multiple quantum Chernoff bound of Li [Ann. Statist. 44 (2016)] by removing its dimension-dependent prefactor. In the asymptotic many-copy regime, our bound proves the achievability of the multiple quantum Chernoff distance for arbitrary separable Hilbert spaces, thereby settling the previously open infinite-dimensional case, and further yields constant-factor sharp asymptotics for the optimal error probability. In binary quantum hypothesis testing, we prove that the minimum error probability is characterized, up to universal constants, by a trace harmonic-mean quantity. Consequently, the optimal binary quantum error probability is within a factor of two of the optimal classical error probability for the associated Nussbaum-Szkoła distributions, complementing the lower bound of Nussbaum and Szkoła [Ann. Statist. 37 (2009)].
arXiv:1401.7658, arXiv:1508.06624, arXiv:quant-ph/0607216. We are sorry if the accented character "ł" does not display properly through arXiv's TeX encoding of Metadata
Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph); Functional Analysis (math.FA); Statistics Theory (math.ST)
arXiv:2606.06246 [quant-ph]
(or arXiv:2606.06246v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.06246 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 209 words
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