Multipartite Leggett-type Inequalities

TL;DR

This paper derives new multipartite Leggett-type inequalities using two approaches, extending previous two-qubit results, and aims to facilitate experimental tests of non-local realism in multi-qubit systems.

Contribution

It introduces two novel methods to derive multipartite Leggett-type inequalities, broadening the scope of non-local realism tests beyond two-qubit systems.

Findings

Derived multipartite Leggett-type inequalities using two approaches

Provided a framework for experimental testing of non-local realism in multi-qubit systems

Highlighted potential for developing stronger inequalities in future work

Abstract

We use two different approaches to derive multipartite Leggett-type inequalities, which are generalizations of the two-qubit Leggett-type inequality obtained in [Nature Phys. \textbf{4}, 681 (2008)]. The first approach is based on the assumption that the probability distributions should be non-negative. The second approach is based on a very simple algebraic equation and is, to some extent, easier than the first approach. Although these inequalities might not be the optimal ones in the sense that their quantum violations may not be the strongest, our results make the first step of generalizing Leggett-type inequality to multi-qubit systems and provide the possibility to experimentally test non-local realism in such systems. Moreover, the two approaches here may shed new light on the challenging problem of obtaining stronger multipartite Leggett-type inequalities.