Moments of<i>P</i>functions and nonclassical depths of quantum states

Abstract

The practical aspect of the moment problem of the P function is developed; i.e., a simple explicit expression for the P function in terms of its moments and the derivatives of the Dirac \ensuremath{\delta} function in the complex domain is derived. Its connection with the concept of the nonclassical depth of a quantum state introduced recently is explored. The basic formulas derived are used in the calculations of several specific examples that are popular in the quantum-optics community, such as photon-number state, binomial state, two-photon thermal state, squeezed-vacuum state, etc.