Robust multi-hypothesis quantum-state discrimination under unknown common unitary perturbations via least favorable priors

• URL: http://arxiv.org/abs/2609.04020v1
• Date: Thu, 03 Sep 2026 15:59:59 GMT
• Title: Robust multi-hypothesis quantum-state discrimination under unknown common unitary perturbations via least favorable priors
• Abstract summary: We study robust K-ary quantum-state discrimination when all candidate states are affected by the same unknown common unitary perturbation.<n>The unknown perturbation does not represent the label to be identified, but acts as a nuisance factor that changes the performance of a fixed measurement.
• Score: 0.40180395587330325
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study robust K-ary quantum-state discrimination when all candidate states are affected by the same unknown common unitary perturbation. The unknown perturbation does not represent the label to be identified, but acts as a nuisance factor that changes the performance of a fixed measurement. We formulate the problem as a minimax decision problem over the possible perturbations and propose using the Bayes-optimal collective measurement associated with a least favorable prior (LFP) on the nuisance-parameter space. For a finite discretization of this space, we show that the LFP can be computed by a semidefinite program and that the corresponding value coincides with the finite-grid minimax success probability. As numerical demonstrations, we consider a binary nonorthogonal qubit model and a nonorthogonal three-state qutrit model with an unknown common unitary perturbation. The LFP-based measurement substantially flattens the success-probability profile and improves the worst-case success probability compared with a reference-point optimal measurement and a uniform-prior Bayes measurement. The resulting LFP concentrates its weight on regions of the nuisance-parameter space that actively limit the robust discrimination performance, thereby providing both a constructive measurement design and a diagnostic description of the difficult nuisance-parameter regimes.

Related papers

• Quantum Decision Theory for Displacement Detection with Finite-Energy GKP States [46.2474896050764]
  We develop a framework for detecting phase-space displacements with finite-energy, $d$-level Gottesman-Kitaev-Preskill (GKP) probes.<n>For single-mode and entanglement-assisted architectures, we derive the Bayesian minimum-error probability.<n>We benchmark the resulting protocols against coherent-state, direction-matched squeezed-vacuum, and twin-beam schemes.
  arXiv  Detail & Related papers  (2026-08-08T10:32:05Z)
• Proximal Mediation Analysis with Hidden Recanting Witnesses [6.9475003037956435]
  Many practical settings rely on the assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori.<n>We develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses.
  arXiv  Detail & Related papers  (2026-06-16T07:07:06Z)
• Genuine Multipartite Nonlocality for Arbitrary Input: Maximal Randomness Generation and Robust Self-Testing [0.0]
  We introduce a Bell inequality capable of identifying genuine multipartite nonlocality (GMNL) in an arbitrary m-partite scenario.<n>We show that our framework enables the extraction of maximal global DI randomness (m bits) at the optimal quantum violation.
  arXiv  Detail & Related papers  (2026-06-09T14:45:31Z)
• Measurement-Incompatibility Constraints for Maximal Randomness [5.560127372386599]
  Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies.<n>Here, we introduce a generalized framework to directly certify maximal randomness from observed probability distributions across systems with arbitrary user numbers.<n>Our results establish a versatile and experimentally accessible route to scalable randomness certification, with implications for quantum cryptography and the physics of nonlocal correlations.
  arXiv  Detail & Related papers  (2025-05-23T07:45:11Z)
• Best Arm Identification with Fixed Budget: A Large Deviation Perspective [54.305323903582845]
  We present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms. In particular, we present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms.
  arXiv  Detail & Related papers  (2023-12-19T13:17:43Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Optimal estimation of pure states with displaced-null measurements [0.0]
  We revisit the problem of estimating an unknown parameter of a pure quantum state. We investigate null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.
  arXiv  Detail & Related papers  (2023-10-10T16:46:24Z)
• Monotonicity and Double Descent in Uncertainty Estimation with Gaussian Processes [52.92110730286403]
  It is commonly believed that the marginal likelihood should be reminiscent of cross-validation metrics and that both should deteriorate with larger input dimensions. We prove that by tuning hyper parameters, the performance, as measured by the marginal likelihood, improves monotonically with the input dimension. We also prove that cross-validation metrics exhibit qualitatively different behavior that is characteristic of double descent.
  arXiv  Detail & Related papers  (2022-10-14T08:09:33Z)
• Inference on Strongly Identified Functionals of Weakly Identified Functions [71.42652863687117]
  We study a novel condition for the functional to be strongly identified even when the nuisance function is not. We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
  arXiv  Detail & Related papers  (2022-08-17T13:38:31Z)
• Partial Identification with Noisy Covariates: A Robust Optimization Approach [94.10051154390237]
  Causal inference from observational datasets often relies on measuring and adjusting for covariates. We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification. Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.
  arXiv  Detail & Related papers  (2022-02-22T04:24:26Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)

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.