相关论文: Wehrl-type coherent state entropy inequalities for…

The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group $SU(2)$, is further extended here to symmetric representations…

We investigate the sharp functional inequalities for the coherent state transforms of $SU(N,1)$. These inequalities are rooted in Wehrl's definition of semiclassical entropy and his conjecture about its minimum value. Lieb resolved this…

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,…

We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group and then by Lieb and…

We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on…

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…

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…

We review Wehrl's definition of a semiclassical entropy in terms of coherent states and give an introductory overview of Lieb's conjecture, its proof (including earlier results), generalizations, and the role of covariant quantum channels…

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 Wehrl entropy construction is proposed for an arbitrary locally compact abelian group $G$. It is proved that the Wehrl entropy is not less than a non-negative integer, which is an invariant of the group $G$. The minimum of the Wehrl…

A new proof for the completeness of the coherent states $D(\alpha )\mid f>$ for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is presented. Generalizations of these results and their consequences are disussed.

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…

The Wehrl entropy of a quantum state is the Shannon entropy of its coherent-state distribution function, and remains non-zero even for pure states. We investigate the relationship between this entropy and the many-particle quantum…

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…

New quantal states which interpolate between the coherent states of the Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states are obtained as the coherent states of a closed and symmetric algebra which interpolates…

Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group $SL(d+1,\C)$. Both are obtained from the K\"ahler potential of the underlying geometry of the sphere corresponding to the…

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…

Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding between two Bergman spaces of the upper-half plane. A question in relation with a Werhl-type entropy inequality for the affine $AX+B$ group.…

For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitation thereof. We give a unified formula for this entropy in terms of single-particle…

We show that a homogeneous convolution kernel on an arbitrary homogeneous group which is L \log L on the unit annulus is bounded on L^p for 1 < p < \infty and is of weak-type (1,1), generalizing the result of Seeger. The proof is in a…