The Wehrl-type entropy conjecture for symmetric $SU(N)$ coherent states: cases of equality and stability

• URL: http://arxiv.org/abs/2412.10940v2
• Date: Mon, 23 Dec 2024 10:49:29 GMT
• Title: The Wehrl-type entropy conjecture for symmetric $SU(N)$ coherent states: cases of equality and stability
• Authors: Fabio Nicola, Federico Riccardi, Paolo Tilli,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Lieb and Solovej proved that, for the symmetric $SU(N)$ representations, the corresponding Wehrl-type entropy is minimized by symmetric coherent states. However, the uniqueness of the minimizers remained an open problem when $N\geq 3$. In this note we complete the proof of the Wehrl entropy conjecture for such representations, by showing that symmetric coherent states are, in fact, the only minimizers. We also provide an application to the maximum concentration of holomorphic polynomials and deduce a corresponding Faber-Krahn inequality. A sharp quantitative form of the bound by Lieb and Solovej is also proved.

Related papers

• Universal chain rules from entropic triangle inequalities [1.8416014644193066]
  We lower bound the smooth min-entropy of an $n$-partite system in terms of, roughly speaking, equally strong entropies of the individual subsystems.<n>We also prove an approximate version of the entropy accumulation theorem, which relaxes the conditions required on the state to bound its smooth min-entropy.
  arXiv  Detail & Related papers  (2024-12-09T18:10:28Z)
• Symmetry-Resolved Relative Entropy of Random States [0.0]
  We calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior.
  arXiv  Detail & Related papers  (2024-11-03T09:16:24Z)
• Multipartite entanglement in the diagonal symmetric subspace [41.94295877935867]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. We present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension.
  arXiv  Detail & Related papers  (2024-03-08T12:06:16Z)
• Taming under isoperimetry [0.0]
  In this article we propose a Langevin-based scheme calledmathbfsTULA$ to sample from distributions with growing log. We derive non-asymientKL and consequently consequently satisfy a Log-Sobolev inequality.
  arXiv  Detail & Related papers  (2023-11-15T14:44:16Z)
• Smooth min-entropy lower bounds for approximation chains [0.0]
  We prove a simple entropic triangle inequality, which allows us to bound the smooth min-entropy of a state in terms of the R'enyi entropy of an arbitrary auxiliary state. Using this triangle inequality, we create lower bounds for the smooth min-entropy of a state in terms of the entropies of its approximation chain in various scenarios.
  arXiv  Detail & Related papers  (2023-08-22T18:55:16Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians [0.0]
  We show that the magnitude of the negative $O(1)$ correction is only slightly greater than the one predicted for random pure states. We derive a simple expression that describes the numerically observed $nu$ dependence of the $O(1)$ deviation from the prediction for random pure states.
  arXiv  Detail & Related papers  (2023-03-23T18:00:02Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• $O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks [107.86545461433616]
  We propose permutation-equivariant architectures, on which a determinant Slater is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function. We substitute the Slater with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N2)$.
  arXiv  Detail & Related papers  (2022-05-26T07:44:54Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Convergence Analysis of Riemannian Stochastic Approximation Schemes [39.32179384256228]
  This paper analyzes a class of correlated approximation (SA) schemes to tackle optimization problems. We show that the conditions we derive are considerably milder than previous works. Third, we consider the case where the mean-field function can only be estimated up to a small bias, and/or the case in which the samples are drawn from a chain.
  arXiv  Detail & Related papers  (2020-05-27T11:24:58Z)
• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing [0.0]
  We present a method to solve the quantum marginal problem for symmetric $d$-level systems. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies.
  arXiv  Detail & Related papers  (2020-01-13T18:20:53Z)

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.