Nonlocality for Generic Networks

TL;DR

This paper introduces a novel class of strategies called Color-Matching for generating nonlocal correlations in quantum networks, establishing a connection between network nonlocality and graph theory, especially graph coloring.

Contribution

It provides the first class of strategies for producing network nonlocality in generic networks and links these strategies to graph theoretical concepts like rigidity and coloring.

Findings

Color-Matching strategies produce nonlocal correlations in networks.

A deep connection between network nonlocality and graph theory is established.

The work introduces the concept of rigidity in classical strategies within networks.

Abstract

Bell's theorem shows that correlations created by a single entangled quantum state cannot be reproduced classically. Such correlations are called Nonlocal. They are the elementary manifestation of a broader phenomenon called Network Nonlocality, where several entangled states shared in a network create Network Nonlocal correlations. In this paper, we provide the first class of strategies producing nonlocal correlations in generic networks. In these strategies, called Color-Matching (CM), any source takes a color at random or in superposition, where the colors are labels for a basis of the associated Hilbert space. A party (besides other things) checks if the color of neighboring sources match. We show that in a large class of networks without input, well-chosen quantum CM strategies result in nonlocal correlations that cannot be produced classically. For our construction, we introduce the graph theoretical concept of rigidity of classical strategies in networks, and using the Finner inequality, establish a deep connection between network nonlocality and graph theory. In particular, we establish a link between CM strategies and the graph coloring problem. This work is extended in a longer paper, Network Nonlocality via Rigidity of Token-Counting and Color-Matching, where we introduce a second family of rigid strategies called Token-Counting, leading to network nonlocality.