Wehrl information entropy and phase distributions of Schrödinger cat and cat-like states

Abstract

The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schr\"odinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schr\"odinger cats (including even, odd and Yurke-Stoler coherent states), as well as the cat-like states generated in Kerr medium are analyzed in detail. It is shown that, in contrast to the Wehrl entropy, the Wehrl phase distribution properly distinguishes between different superpositions of unequally-weighted states in respect to their number and phase-space configuration.