Towards a minimal example of quantum nonlocality without inputs

TL;DR

This paper investigates the simplest possible quantum nonlocality scenarios in network settings without measurement inputs, focusing on the triangle network with minimal output sizes, and explores the potential for binary-output examples.

Contribution

It provides minimal examples of quantum nonlocality without inputs in the triangle network, including specific output cardinalities, and discusses prospects for binary-output cases.

Findings

Examples with output sizes 3-3-3 and 3-3-2 demonstrate nonlocality without inputs.

Discussion on the possibility of binary-output nonlocality in the triangle network.

Connection established between nonlocality examples and the Lovász local lemma.

Abstract

The network scenario offers interesting new perspectives on the phenomenon of quantum nonlocality. Notably, when considering networks with independent sources, it is possible to demonstrate quantum nonlocality without the need for measurements inputs, i.e. with all parties performing a fixed quantum measurement. Here we aim to find minimal examples of this effect. Focusing on the minimal case of the triangle network, we present examples involving output cardinalities of $3-3-3$ and $3-3-2$. Finally, we discuss the prospects of finding an example of quantum nonlocality in the triangle network with binary outputs, and point out a connection to the Lovasz local lemma.