Degree of Nonclassical Behaviour

Abstract

In classical physics the description of a system by a phase-space probability distribution is a useful tool. Glauber and Cahill [1,2] introduced a similar description for quantum mechanics generalizing earlier work by Wigner, Husimi and others. This description is useful for all systems which can be described in terms of bosonic or harmonic oscillator creation and destruction operators. There are two principal differences between classical and quantum phase-space. The first is, that the quantum analogue of the classical probability distribution is no longer positive definite. Hence we will refer to it as quasiprobability distribution, or quasidistribution for short. Secondly, the appropriate quasidistributions to use for calculating the expectation values of an operator depends on the ordering of the creation and annihilation operators. There are quasidistributions for all orderings continuously characterized by the ordering parameter s.