Beyond the Magic Square Game: Widening the Gap for Two Bell States

TL;DR

This paper constructs a nonlocal game with a larger quantum-classical gap than the Magic Square game, using two Bell states and symmetry of the 2-qubit Pauli group, advancing understanding of quantum nonlocality.

Contribution

It introduces a new nonlocal game with an improved quantum-classical gap, leveraging symmetry and two Bell states, surpassing previous results.

Findings

Quantum-classical gap at least 4/35

Classical value of the game is 31/35

Uses symmetry of the 2-qubit Pauli group

Abstract

We demonstrate that the largest gap between the entangled value and the classical value for a one-round two-player nonlocal game with a perfect entangled strategy using two Bell states of entanglement is at least $\frac{4}{35}$, improving on the gap of $\frac{1}{9}$ achieved by the Mermin-Peres magic square game. We do so by explicitly constructing a nonlocal game with classical value $\frac{31}{35}$ using the full symmetry of the 2-qubit Pauli group.