Resource theory of asymmetric distinguishability with partial information

• URL: http://arxiv.org/abs/2510.02071v2
• Date: Fri, 03 Oct 2025 06:42:55 GMT
• Title: Resource theory of asymmetric distinguishability with partial information
• Authors: Siqi Yao, Kun Fang,
• Abstract summary: Worst-case quantum divergence is a key measure in quantum information.<n>We show that divergences can be understood from the perspective of the resource theory of asymmetric distinguishability.<n>We extend this framework to settings with partial information.
• Score: 2.0094233004333124
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent studies have introduced the worst-case quantum divergence as a key measure in quantum information. Here we show that such divergences can be understood from the perspective of the resource theory of asymmetric distinguishability, which utilizes the asymmetric distinguishability between a pair of quantum states as resource. In our work, we extend this framework to settings with partial information, where the goal is to distinguish between sets of quantum states rather than individual states. Within this setting, we characterize optimal rates for resource distillation and dilution using (smoothed) one-shot divergences and regularized divergences. Our framework further exhibits a reversibility property: resource interconversions can be achieved without loss at rates determined entirely by regularized divergences. These results offer a broad operational interpretation of divergences between state sets and generalize existing resource theories to encompass incomplete information scenarios.

Related papers

• Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits [72.0643009153473]
  We show that expressive variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size.<n>As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions.<n>We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class.
  arXiv  Detail & Related papers  (2026-01-05T08:04:33Z)
• Unified quantification of entanglement and magic in information scrambling and their trade-off relationship [1.6574413179773757]
  Information scrambling is a phenomenon observed in a wide range of quantum systems.<n>We introduce a measure of the two types of scrambling, grounded in resource-theoretic principles.
  arXiv  Detail & Related papers  (2025-08-16T08:09:45Z)
• A unified framework of unitarily residual measures for quantifying dissipation [1.6574413179773757]
  We introduce a framework for quantifying the dissipation by isolating the non-unitary components of quantum dynamics.<n>Our results provide a powerful tool for quantifying dissipation in open quantum systems, advancing the understanding of quantum thermodynamics.
  arXiv  Detail & Related papers  (2024-12-03T08:00:24Z)
• The relative entropy of coherence quantifies performance in Bayesian metrology [0.21111026813272177]
  We show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence is equal to the difference between the information gained, and the optimal Holevo information.
  arXiv  Detail & Related papers  (2024-01-29T10:11:15Z)
• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• The i.i.d. State Convertibility in the Resource Theory of Asymmetry for Finite Groups [0.0]
  We derive both the exact and approximate conversion rates between i.i.d. states.<n>We show that the approximate conversion rate either diverges or equals zero.
  arXiv  Detail & Related papers  (2023-12-25T15:42:24Z)
• Enriching Disentanglement: From Logical Definitions to Quantitative Metrics [59.12308034729482]
  Disentangling the explanatory factors in complex data is a promising approach for data-efficient representation learning. We establish relationships between logical definitions and quantitative metrics to derive theoretically grounded disentanglement metrics. We empirically demonstrate the effectiveness of the proposed metrics by isolating different aspects of disentangled representations.
  arXiv  Detail & Related papers  (2023-05-19T08:22:23Z)
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication [60.18814584837969]
  We introduce the notion of q-compatibility, which unifies different notions of POVMs, channels, and instruments incompatibility. We are able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.
  arXiv  Detail & Related papers  (2022-11-16T21:33:31Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• R\'enyi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations [91.3755431537592]
  We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence. We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
  arXiv  Detail & Related papers  (2021-06-19T04:06:23Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Fundamental Limits and Tradeoffs in Invariant Representation Learning [99.2368462915979]
  Many machine learning applications involve learning representations that achieve two competing goals. Minimax game-theoretic formulation represents a fundamental tradeoff between accuracy and invariance. We provide an information-theoretic analysis of this general and important problem under both classification and regression settings.
  arXiv  Detail & Related papers  (2020-12-19T15:24:04Z)

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.