Multiple Quantum Hypothesis Testing: One-Shot Pairwise Bounds and Sharp Asymptotics

• URL: http://arxiv.org/abs/2606.06246v1
• Date: Thu, 04 Jun 2026 14:49:12 GMT
• Title: Multiple Quantum Hypothesis Testing: One-Shot Pairwise Bounds and Sharp Asymptotics
• Abstract summary: We establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors.<n>We prove that the minimum error probability is characterized, up to universal constants, by a trace harmonic-mean quantity.
• Score: 13.098901971644656
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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)].

Related papers

• Optimal Error Exponents for Composite Sequential Quantum Hypothesis Testing [1.376408511310322]
  We propose a mixture-sequential quantum probability ratio test that adaptively selects measurements based on the current mixture estimate of the alternative set.<n>Under an expected sample size constraint, we show that our proposed strategy simultaneously achieves the Type-I and (worst-case) Type-II error exponents.
  arXiv  Detail & Related papers  (2026-05-06T13:44:17Z)
• A Berry-Esseen Bound for Quantum Lattice Systems [33.82119899094064]
  We prove a version of the Berry-Esseen theorem for quantum lattice systems.<n>We provide a rigorous convergence estimate towards the normal distribution for large but finite system size.
  arXiv  Detail & Related papers  (2026-05-05T14:58:16Z)
• A Converse Bound via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing [3.1351527202068445]
  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.
  arXiv  Detail & Related papers  (2026-01-20T13:48:28Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• Beyond Hoeffding and Chernoff: Trading conclusiveness for advantages in quantum hypothesis testing [2.046223849354785]
  We study protocols that are permitted a suitably measurement probability of producing an inconclusive discrimination outcome.<n>We show that even by allowing an arbitrarily small probability of inconclusiveness, the limits imposed by the quantum Hoeffding and Chernoff bounds can be significantly exceeded.
  arXiv  Detail & Related papers  (2025-10-08T22:42:11Z)
• Error exponents of quantum state discrimination with composite correlated hypotheses [40.82628972269358]
  We study the error exponents in quantum hypothesis testing between two sets of quantum states.<n>We introduce and compare two natural extensions of the quantum Hoeffding divergence and anti-divergence to sets of quantum states.
  arXiv  Detail & Related papers  (2025-08-18T13:04:06Z)
• Generalized quantum Chernoff bound [1.8371802327210847]
  We establish a quantum Chernoff bound for the discrimination of multiple sets of quantum states.<n>We show that discriminating between sets of quantum states is no harder than discriminating between their worst-case elements in terms of error probability.
  arXiv  Detail & Related papers  (2025-08-18T12:41:04Z)
• On the optimal error exponents for classical and quantum antidistinguishability [3.481985817302898]
  Antidistinguishability has been used to investigate the reality of quantum states. We show that the optimal error exponent vanishes to zero for classical and quantum antidistinguishability. It remains an open problem to obtain an explicit expression for the optimal error exponent for quantum antidistinguishability.
  arXiv  Detail & Related papers  (2023-09-07T14:03:58Z)
• Postselected quantum hypothesis testing [9.131273927745731]
  We study a variant of quantum hypothesis testing wherein an additional 'inconclusive measurement outcome' is added. The error probabilities are conditioned on a successful attempt, with inconclusive trials disregarded. We prove that the error exponent of discriminating any two quantum states $rho$ and $sigma$ is given by the Hilbert projective metric $D_max(|sigma) + D_max(sigma | rho)$ in asymmetric hypothesis testing.
  arXiv  Detail & Related papers  (2022-09-21T18:00:00Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.