Pseudo-diffusion equation and information entropy of squeezed-coherent states

Abstract

As the squeezed-coherent states are labeled by 3-tuple, the momentum, the coordinate and the squeeze parameter, a phase space probability distribution function associated with a generic wavefunction can be introduced. We verify that this probability function is the solution of a partial differential equation, the pseudo-diffusion equation, hence permitting to extend the concept of information entropy, as introduced by Wehrl for the coherent states, to the squeezed-coherent states. It is shown that the entropy functionals can be used as a measure of quantum correlations between the phase space variables, for a given wavefunction; we also present several properties and discuss the use of the entropic inequality as a concept that complements the Heisenberg uncertainty relationship.