Network Nonlocality via Rigidity of Token-Counting and Color-Matching

TL;DR

This paper introduces two generic strategies, Token-Counting and Color-Matching, to produce and analyze network nonlocal correlations without input, demonstrating their rigidity and quantum nonlocality in large networks.

Contribution

It presents the first two generic methods for generating network nonlocal correlations without input and proves their rigidity, enabling the demonstration of quantum nonlocality in broad network classes.

Findings

Token-Counting and Color-Matching strategies are rigid in wide classes of networks.

Quantum implementations of these strategies produce nonlocal correlations unattainable classically.

Examples of network nonlocality without input are provided, highlighting genuine quantum effects.

Abstract

Network Nonlocality is the study of the Network Nonlocal correlations created by several independent entangled states shared in a network. In this paper, we provide the first two generic strategies to produce nonlocal correlations in large classes of networks without input. In the first one, called Token-Counting (TC), each source distributes a fixed number of tokens and each party counts the number of received tokens. In the second one, called Color-Matching (CM), each source takes a color and a party checks if the color of neighboring sources match. Using graph theoretic tools and Finner's inequality, we show that TC and CM distributions are rigid in wide classes of networks, meaning that there is essentially a unique classical strategy to simulate such correlations. Using this rigidity property, we show that certain quantum TC and CM strategies produce correlations that cannot be produced classicality. This leads us to several examples of Network Nonlocality without input. These examples involve creation of coherence throughout the whole network, which we claim to be a fingerprint of genuine forms of Network Nonlocality. This work extends a more compact parallel work [Nonlocality for Generic Networks, arXiv:2011.02769] on the same subject and provides all the required technical proofs.