Related papers: On the Wehrl entropy lower bound for a locally com…

Lieb and Carlen have shown that mixed states with minimal Wehrl entropy are coherent states. We prove that mixed states with almost minimal Wehrl entropy are almost coherent states. This is proved in a quantitative sense where both the norm…

A lower bound for the Wehrl entropy of a single quantum spin is derived. The high-spin asymptotics of this bound coincides with Lieb's conjecture up to, but not including, terms of first and higher order in the inverse spin quantum number.…

Gnutzmann and Zyczkowski have proposed the Renyi-Wehrl entropy as a generalization of the Wehrl entropy, and conjectured that its minimum is obtained for coherent states. We prove this conjecture for the Renyi index q=2,3,... in the cases…

We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth in https://link.aps.org/doi/10.1103/PhysRevA.104.042211 and https://iopscience.iop.org/article/10.1088/1751-8121/aa852f/meta. Said…

We present analytical results toward the Wigner entropy conjecture, which posits that among all physical Wigner non-negative states the Wigner entropy is minimized by pure Gaussian states for which it attains the value $1+\ln\pi$.Working…

We propose to quantify the entanglement of pure states of $N \times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure…

We discuss the Wehrl-type entropy inequality conjecture for the group $SU(1,1)$ and for its subgroup $AX+B$ (or affine group), their representations on $L^2({\mathbb R}_+)$, and their coherent states. For $AX+B$ the Wehrl-type conjecture…

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure…

The Wehrl entropy is an entropy associated to the Husimi quasi-probability distribution. We discuss how it can be used to formulate entropic uncertainty relations and for a quantification of entanglement in continuous variables. We show…

Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to…

If G is a locally essential subgroup of a compact abelian group K, then: (i) t(G)=w(G)=w(K), where t(G) is the tightness of G; (ii) if G is radial, then K must be metrizable; (iii) G contains a super-sequence S converging to 0 such that…

For a locally compact Abelian group $G$ and a continuous weight function $\omega$ on $G$ we show that the Beurling algebra $L^1(G, \omega)$ is weakly amenable if and only if there is no nontrivial continuous group homomorphism $\phi$: $G\to…

Lieb's conjecture for the Wehrl entropy of Bloch coherent states is proved for spin 1 and spin 3/2. Using a geometric representation we solve the entropy integrals for states of arbitrary spin and evaluate them explicitly in the cases of…

A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it has countably many complete 1-types over every finite subset of G. We show here…

We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…

In this note we present that the patch counting entropy can be obtained as a limit and investigate which sequences of compact sets are suitable to define this quantity. We furthermore present a geometric definition of patch counting entropy…

Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…

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,…

In this note we show that if $G$ is a countably infinite abelian group such that $nG=0$ for some integer $n$, then the only locally minimal group topology on $G$ is the discrete one.