A new nonclassicality measure for the quantum states of a bosonic field

Stephan De Bièvre,Mikhail Kolobov,Giuseppe Patera,Dmitri Horoshko,D Mogilevtsev

doi:10.1051/epjconf/201919800013

Abstract

We review a recently proposed measure of the nonclassicality of a bosonic field, based on the sensitivity of its quasi-probability distributions to ordering of the creation and annihilation operators. We illustrate the new measure by several concrete examples and show its advantages compared to other measures of nonclassicality such as the Wigner function negativity and the entanglement potential.

Highlights

It is well known that quantum theory admits states of the electromagnetic field, not admitted by classical electrodynamics, e.g. the single-photon state and the squeezed state of an optical mode
All possible states of one optical mode are divided in two classes: states having a classical analog, and states having no classical analog
A parameter satisfying the first requirement is known as a “nonclassicality witness”, while the second requirement corresponds to a “nonclassicality measure”

Summary

Introduction

It is well known that quantum theory admits states of the electromagnetic field, not admitted by classical electrodynamics, e.g. the single-photon state and the squeezed state of an optical mode. Negativity of the P-function indicates that the corresponding state is non-classical. The P-function of a nonclassical state may be highly singular. It is strongly desirable to have a parameter which (i) indicates that the measured state is non-classical, and (ii) says how strongly nonclassical the state is, i.e. how far this state is from the class of classical states. In this work we review a recently proposed measure of nonclassicality [2] and compare it with several other such measures on the class of highly nonclassical Schrödinger cat states of an optical field

The s-ordered entropy

The ordering sensitivity

Conclusions