Proof of the Wehrl-type Entropy Conjecture for Symmmetric SU(N) Coherent States

Abstract

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 of the groups $SU(N)$ for all $N$. This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.

15 pages. To appear in Commun. Math. Phys

References in corpus (2)

• Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
• On quantum estimation, quantum cloning and finite quantum de Finetti theorems

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