Pseudo-telepathy games and genuine NS k-way nonlocality using graph states

TL;DR

This paper introduces a new family of pseudo-telepathy games based on graph states, demonstrating their ability to produce nonlocal correlations that cannot be simulated by any finite number of classical or nonlocal resources, extending previous results.

Contribution

It extends the class of pseudo-telepathy games using graph states and proves their non-simulability by k-partite nonlocal boxes for large graphs, advancing understanding of quantum nonlocality.

Findings

A family of pseudo-telepathy games based on graph states is defined.

Certain graph states produce correlations not simulable by any finite nonlocal resources.

The non-simulability extends to large Paley graph states with more than $k^{2}2^{2k-2}$ vertices.

Abstract

We define a family of pseudo-telepathy games using graph states that extends the Mermin games. This family also contains a game used to define a quantum probability distribution that cannot be simulated by any number of PR boxes. We extend this result proving that the probability distribution obtained by the Paley graph state on 13 vertices cannot be simulated by any number of 4-partite non local boxes and that the Paley graph states on more than $k^{2}2^{2k-2}$ vertices provides a probability distribution that cannot be simulated by k-partite nonlocal boxes