An elementary approach to Wehrl-type entropy bounds in quantitative form

• URL: http://arxiv.org/abs/2512.04245v1
• Date: Wed, 03 Dec 2025 20:25:23 GMT
• Title: An elementary approach to Wehrl-type entropy bounds in quantitative form
• Abstract summary: We consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric $SU(N)$ coherent states.<n>We propose an elementary proof of this result, based on reformulating the Wehrl-type entropy as a function defined on the unit sphere in $mathbbCd$, for some suitable $d$, and on some explicit (and somewhat surprising) computations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric $SU(N)$ coherent states, which was obtained only recently by the authors. Here, we propose an elementary proof of this result, based on reformulating the Wehrl-type entropy as a function defined on the unit sphere in $\mathbb{C}^d$, for some suitable $d$, and on some explicit (and somewhat surprising) computations.

Related papers

• Revisiting the Page curve and its moments. A combinatorial approach [0.0]
  We revisit the calculation of the von Neumann (or "entanglement") entropy of a subsystem of a pure quantum state.<n>We derive simple and closed expressions for all power moments, from which the moments of the entropy can be computed by simple differentiation.
  arXiv  Detail & Related papers  (2026-06-29T21:48:28Z)
• Low-degree Lower bounds for clustering in moderate dimension [53.03724383992195]
  We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $mathbbRd$.<n>We show that while the difficulty of clustering for $n leq dK$ is driven by dimension reduction and spectral methods, the moderate-dimensional regime involves more delicate phenomena leading to a "non-optimal rate"<n>We provide a novel non-spectral algorithm matching this rate, shedding new light on the computational limits of the clustering problem in moderate dimension.
  arXiv  Detail & Related papers  (2026-02-26T14:03:55Z)
• Provably Efficient Algorithms for S- and Non-Rectangular Robust MDPs with General Parameterization [85.91302339486673]
  We study robust Markov decision processes (RMDPs) with general policy parameterization under s-rectangular and non-rectangular uncertainty sets.<n>We prove novel Lipschitz and Lipschitz-smoothness properties for general policy parameterizations that extends to infinite state spaces.<n>We design a projected gradient descent algorithm for s-rectangular uncertainty and a Frank-Wolfe algorithm for non-rectangular uncertainty.
  arXiv  Detail & Related papers  (2026-02-11T21:44:20Z)
• Low-degree lower bounds via almost orthonormal bases [47.83594448785856]
  Low-degrees have emerged as a powerful paradigm for providing evidence of statistical--computational gaps across a variety of high-dimensional statistical models.<n>In this work, we propose a more direct proof strategy.
  arXiv  Detail & Related papers  (2025-09-11T11:07:36Z)
• Entropic Mirror Descent for Linear Systems: Polyak's Stepsize and Implicit Bias [55.72269695392027]
  This paper focuses on applying entropic mirror descent to solve linear systems.<n>The main challenge for the convergence analysis stems from the unboundedness of the domain.<n>To overcome this without imposing restrictive assumptions, we introduce a variant of Polyak-type stepsizes.
  arXiv  Detail & Related papers  (2025-05-05T12:33:18Z)
• Towards a Sharp Analysis of Offline Policy Learning for $f$-Divergence-Regularized Contextual Bandits [49.96531901205305]
  We analyze $f$-divergence-regularized offline policy learning.<n>For reverse Kullback-Leibler (KL) divergence, we give the first $tildeO(epsilon-1)$ sample complexity under single-policy concentrability.<n>We extend our analysis to dueling bandits, and we believe these results take a significant step toward a comprehensive understanding of $f$-divergence-regularized policy learning.
  arXiv  Detail & Related papers  (2025-02-09T22:14:45Z)
• The Wehrl-type entropy conjecture for symmetric $SU(N)$ coherent states: cases of equality and stability [0.0]
  We prove that for symmetric $SU(N)$ representations, the corresponding Wehrl-type entropy is minimized by coherent states.<n>A sharp quantitative form of the bound by Lieb and Solovej is also proved.
  arXiv  Detail & Related papers  (2024-12-14T19:33:08Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences [45.935798913942904]
  The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is presented. Examples of the solution for particular choices of the function $f$ are presented.
  arXiv  Detail & Related papers  (2024-02-01T11:12:00Z)
• A characterization of von Neumann entropy using functors [0.0]
  We propose a method for characterizing von Neumann entropy by extending their results to quantum systems. In this paper we consider a functor from a certain category to the monoid of non-negative real numbers with addition as a map from measure-preserving functions to non-negative real numbers.
  arXiv  Detail & Related papers  (2023-09-19T06:26:19Z)
• Modular Nuclearity and Entanglement Entropy [0.0]
  In this work we show that the Longo's canonical entanglement entropy is finite in any local QFT verifying a modular $p$-nuclearity condition. As application, in $1+1$-dimensional integrable models with factorizing S-matrices we study the behavior of the canonical entanglement entropy as the distance between two causally disjoint wedges diverges.
  arXiv  Detail & Related papers  (2021-08-20T09:01:59Z)
• Kurtosis of von Neumann entanglement entropy [2.88199186901941]
  We study the statistical behavior of entanglement in quantum bipartite systems under the Hilbert-Schmidt ensemble. The main contribution of the present work is the exact formula of the corresponding fourth cumulant that controls the tail behavior of the distribution.
  arXiv  Detail & Related papers  (2021-07-21T22:20:10Z)
• Towards a functorial description of quantum relative entropy [0.0]
  Affine functor defines an affine functor in the special case where the relative entropy is finite. A recent non-commutative disintegration theorem provides a key ingredient in this proof.
  arXiv  Detail & Related papers  (2021-05-10T00:58:46Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)

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.