Leggett-Garg inequalities for testing quantumness of gravity

TL;DR

This paper investigates how gravitational interactions in a hybrid quantum system can lead to violations of Leggett-Garg inequalities, providing insights into the quantum nature of gravity through quasiprobability analysis.

Contribution

It demonstrates that gravitational interaction can cause violations of Leggett-Garg inequalities in a hybrid system, highlighting conditions for such violations and their potential detectability.

Findings

Gravitational interaction can violate Leggett-Garg inequalities in hybrid systems.

Entanglement generated by gravity suppresses inequality violations at initial times.

Proper parameter choices enable observable violations of Leggett-Garg inequalities.

Abstract

In this study, we determine a violation of the Leggett-Garg inequalities due to gravitational interaction in a hybrid system consisting of a harmonic oscillator and a spatially localized superposed particle. The violation of the Leggett-Garg inequalities is discussed using the two-time quasiprobability in connection with the entanglement negativity generated by gravitational interaction. It is demonstrated that the entanglement suppresses the violation of the Leggett-Garg inequalities when one of the two times of the quasiprobability t_1 is chosen as the initial time. Further, it is shown that the Leggett-Garg inequalities are generally violated due to gravitational interaction by properly choosing the configuration of the parameters, including t_1 and t_2, which are the times of the two-time quasiprobability. The feasibility of detecting violations of the Leggett-Garg inequalities in hybrid systems is also discussed.