Leggett-Garg inequalities with deformed Pegg-Barnett phase observables

TL;DR

This paper explores the violation of Leggett-Garg inequalities in a boson system with deformed Pegg-Barnett phase observables, analyzing the effects of dissipation and initial states on quantum nonclassicality.

Contribution

It introduces a method to test LGIs using deformed phase operators and the quantum Fourier transform, providing explicit forms and analyzing dissipation effects.

Findings

LGI violations depend on initial states and time differences

Violations persist at large amplitudes without dissipation

Dissipation rapidly diminishes LGI violations

Abstract

We investigate the Leggett-Garg inequalities (LGIs) for a boson system whose observables are given by deforming the Pegg-Barnett phase operators. We consider two observables and show that the quantum Fourier transform is useful in the realization of the required measurements. Deriving explicit forms for the LGIs using the coherent state $|\alpha\rangle$ as the initial state, we explore the regimes where they are violated when the time difference between observations of the phase operators is varied. We show that the system remains nonclassical in the large amplitude limit without dissipation, however with dissipation, our violation diminishes rapidly.