The minimal example of quantum network Bell nonlocality

TL;DR

This paper identifies the smallest quantum network configuration, the triangle network, capable of exhibiting Bell nonlocality with binary outcomes and no input choices, advancing understanding of quantum correlations.

Contribution

It demonstrates quantum nonlocality in the minimal triangle network and develops an efficient method to model quantum distributions in such networks.

Findings

Quantum nonlocality exists in the triangle network with binary outcomes.

An explicit quantum model reproduces target distributions with machine precision.

The method provides insights into generating nonlocal distributions in quantum networks.

Abstract

In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum networks.