Entropic Uncertainty Relations for Mutually Unbiased Operator Frames

• URL: http://arxiv.org/abs/2606.23185v1
• Date: Mon, 22 Jun 2026 11:30:18 GMT
• Title: Entropic Uncertainty Relations for Mutually Unbiased Operator Frames
• Abstract summary: We develop an operator-frame formulation of entropic uncertainty relations in the Hilbert-Schmidt space of operators.<n>For general continuous indexed operator frames, we derive an entropic uncertainty relation for the associated coefficient distributions.
• Score: 1.7188280334580195
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop an operator-frame formulation of entropic uncertainty relations in the Hilbert-Schmidt space of operators. For general continuous indexed operator frames, we derive an entropic uncertainty relation for the associated coefficient distributions by combining endpoint norm estimates with Riesz-Thorin interpolation. We then identify a distinguished class of mutually unbiased operator frames, defined through constant-modulus trace overlaps. Under suitable structural conditions, the corresponding coefficient amplitudes are related by a bilinear Fourier transform, leading to a stronger Hirschman-Beckner-type entropic uncertainty relation. As canonical realizations, we consider Weyl displacement operators and Wigner kernels, as well as Cartesian dyadic frames generated by position and momentum eigenstates. These examples recover familiar continuous-variable Fourier dualities while extending entropic uncertainty relations beyond measurement outcomes to operator representations themselves.

Related papers

• Contraction Analysis of Holomorphic Dynamical Systems via the Intrinsic Kobayashi Metric [0.0]
  This paper studies incremental stability of holomorphic dynamical systems through the infinitesimal Kobayashi metric.<n>Contraction is formalized as an upper Dini-derivative inequality on the Kobayashi metric along trajectories.
  arXiv  Detail & Related papers  (2026-08-01T17:06:21Z)
• Quotient-Categorical Representations for Bellman-Compatible Average-Reward Distributional Reinforcement Learning [8.988097534171995]
  We introduce a quotient-space formulation in which state-indexed bias laws are identified up to a common translation.<n>We show that synchronous exact updates are gain-independent at the quotient-law level.
  arXiv  Detail & Related papers  (2026-05-11T22:17:09Z)
• Page Curve for Local-Operator Entanglement from Free Probability [0.0]
  Local-operator entanglement measures the classical simulability of Heisenberg operators.<n>We analytically compute its value for Haar random dynamics for all Rényi indices.<n>In contrast to higher-order out-of-time ordered correlators, the leading-order LOE is independent of the initial operator.
  arXiv  Detail & Related papers  (2026-05-04T18:00:00Z)
• Feynman's linear divergence problem [45.88028371034407]
  We construct secondary generalized scattering operators for the related case of linear divergence in QED.<n>This gives a positive answer to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED.
  arXiv  Detail & Related papers  (2026-04-13T15:19:27Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Graph Structured Operator Inequalities and Tsirelson-Type Bounds [0.0]
  inequalities generalize the analytic structure underlying the Tsirelson and CHSH bounds.<n>A graph based formulation captures sparse interaction patterns via constants depending only on graph connectivity.<n>Results link analytic operator inequalities with quantum information settings such as Bell correlations and network nonlocality.
  arXiv  Detail & Related papers  (2025-11-03T12:41:00Z)
• An Empirical Bernstein Inequality for Dependent Data in Hilbert Spaces and Applications [29.897642835989117]
  We introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert space.<n>Our inequalities apply to both stationary and non-stationary processes.
  arXiv  Detail & Related papers  (2025-07-10T14:58:28Z)
• Stronger sum uncertainty relations for non-Hermitian operators [3.62592308328482]
  This study presents the sum URs for non-Hermitian operators acting on system states using an appropriate Hilbert-space metric.<n>The developed methods and results can help give an in-depth understanding of the usefulness of G-metric formalism in non-Hermitian quantum mechanics.
  arXiv  Detail & Related papers  (2024-07-30T00:58:23Z)
• 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)
• Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces [52.35063796758121]
  We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We link the risk with the estimation of the spectral decomposition of the Koopman operator. Our results suggest RRR might be beneficial over other widely used estimators.
  arXiv  Detail & Related papers  (2022-05-27T14:57:48Z)
• 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)
• Entropic Bounds as Uncertainty Measure of Unitary Operators [0.0]
  We show how distinguishable operators are compatible while maximal incompatibility of unitary operators can be connected to bases for some subspaces of operators which are mutually unbiased.
  arXiv  Detail & Related papers  (2020-11-24T01:38:44Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.