Quantifying multipartite nonlocality via the size of the resource

TL;DR

This paper introduces a method to quantify the minimal number of parties needed to share nonlocal resources for generating correlations, using the concept of minimal group size and Bell-like inequality lifting.

Contribution

It proposes a general recipe to construct minimal group size witnesses from Bell-like inequalities and demonstrates their applicability to non-signaling resources.

Findings

MGS can be determined using the proposed recipe and numerical methods.

Non-signaling resources are as powerful as signaling ones within full-correlation functions.

Explicit examples illustrate the effectiveness of the approach.

Abstract

The generation of (Bell-)nonlocal correlations, i.e., correlations leading to the violation of a Bell-like inequality, requires the usage of a nonlocal resource, such as an entangled state. When given a correlation (a collection of conditional probability distributions) from an experiment or from a theory, it is desirable to determine the extent to which the participating parties would need to collaborate nonlocally for its (re)production. Here, we propose to achieve this via the minimal group size (MGS) of the resource, i.e., the smallest number of parties that need to share a given type of nonlocal resource for the above-mentioned purpose. In addition, we provide a general recipe --- based on the lifting of Bell-like inequalities --- to construct MGS witnesses for non-signaling resources starting from any given ones. En route to illustrating the applicability of this recipe, we also show that when restricted to the space of full-correlation functions, non-signaling resources are as powerful as unconstrained signaling resources. Explicit examples of correlations where their MGS can be determined using this recipe and other numerical techniques are provided.