Faithful test of non-local realism with entangled coherent states

TL;DR

This paper explores the violation of Leggett's inequality using entangled coherent states, establishing a connection with Bell's inequality violations and generalizing Leggett's bounds to higher-dimensional systems.

Contribution

It provides a mathematical relation between Bell's and Leggett's inequalities, extends Leggett's bounds to larger Hilbert spaces, and introduces an optimization method for stronger violations.

Findings

Established relation between Bell and Leggett inequalities violations.

Generalized Leggett's bounds to higher-dimensional systems.

Developed an optimization technique for measurement settings.

Abstract

We investigate the violation of Leggett's inequality for non-local realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the non-local realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original arguments to continuous-variable states.