A New Theorem on the Nonclassicality of States

TL;DR

This paper introduces a new theorem linking the zeros of the s-parameterized quasiprobability distribution to the non-classicality depth of quantum states, providing a theoretical basis for generating states with arbitrary non-classicality.

Contribution

It presents a novel theorem connecting quasiprobability distribution zeros to non-classicality depth, enhancing understanding of quantum state non-classicality and its manipulation.

Findings

Theorem relates zeros of Wigner function to non-classicality depth.

Provides a method to determine non-classicality depth from phase-space distributions.

Analyzes effects of photon addition and subtraction on non-classicality.

Abstract

A new theorem on the non-classicality depth of states has been proved. We show that if $W_{\hat \rho} (\alpha_m,s_m)=0$ exist for some value of the ordering parameter $s$ at some phase-space point $\alpha_m$, and if $W_{\hat \rho} (\alpha,s_m)$ is an acceptable quasi-classical distribution, the non-classicality of $\hat \rho$ in parallel with Lee's non-classicality depth is then given by $\tau_m=(1 - s_m)/2$. In this way, a general examination of the effects of the single-photon-addition and -subtraction operations has been studied. The theorem, indeed, provides a theoretical background for generating quantum states of arbitrary non-classicality depth.