Equivalence between Bell inequalities and quantum Minority game

TL;DR

This paper establishes a direct equivalence between maximizing payoffs in a four-player quantum Minority game and violating Bell inequalities, revealing a unique link between quantum game strategies and quantum nonlocality.

Contribution

It demonstrates a novel correspondence between Bell inequalities and quantum game strategies specifically for the four-player quantum Minority game.

Findings

Payoff maximization corresponds to Bell inequality violation.

The correspondence is unique to the four-player Minority game.

The game highlights the role of Bell nonlocality in quantum strategic interactions.

Abstract

We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality with each observer choosing the same set of two dichotomic observables. We conclude the existence of direct correspondences between (i) the payoff rule and Bell inequalities, and (ii) the strategy and the choice of measured observables in evaluating these Bell inequalities. We also show that such a correspondence between Bell polynomials (in a single plane) and four-player, symmetric, binary-choice quantum games is unique to the four-player quantum Minority game and its "anti-Minority" version. This indicates that the four-player Minority game not only plays a special role among quantum games but also in studies of Bell-type quantum nonlocality.