Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel

TL;DR

This paper investigates how parity symmetry in superpositions of spin coherent states is affected by Gaussian noise, revealing that higher spin values and decoherence intensify symmetry breaking.

Contribution

It provides a detailed analysis of parity symmetry breaking in spin-$j$ coherent state superpositions under Gaussian noise, extending understanding from spin-$1/2$ to general spin-$j$ systems.

Findings

Parity asymmetry correlates with increasing spin $j$.

Higher decoherence parameter $s$ enhances parity symmetry violation.

Parity symmetry breaking is more pronounced in higher spin states.

Abstract

The Wigner function and Wigner-Yanase skew information are connected through quantum coherence. States with high skew information often exhibit more pronounced negative regions in their Wigner functions, indicative of quantum interference and non-classical behavior. Thus, the relationship between these two concepts is that states with high quantum coherence tend to display more non-classical features in their Wigner functions. By exploiting this relationship, which manifests as parity symmetry and asymmetry, we analyze parity symmetry and asymmetry in the superposition of two spin coherent states for a spin-$1/2$, as well as for a general spin-$j$. This analysis shows that the preservation of the parity asymmetry, or the violation of the parity symmetry, correlates with an increase in the value of spin $j$. Additionally, we investigate the behavior of parity symmetry and asymmetry of these states subjected to a Gaussian noise channel. Specifically, we examine how this parity symmetry and asymmetry change and identify the points at which parity symmetry is violated in the spin-$1/2$ cat state. Notably, the violation of parity symmetry becomes more pronounced at higher values of the decoherence parameter $s$. Our study shows how the spin value $j$ affects the breaking of parity symmetry in general spin-$j$ cat states that are hit by Gaussian noise.