Entanglement witness game

TL;DR

This paper introduces an entanglement witness game, a quantum game that detects entanglement through payoff, extending the concept of semi-quantum nonlocal games and relating to CHSH nonlocality.

Contribution

It proposes a novel entanglement witness game framework that links entanglement detection with game-theoretic payoff, inspired by Buscemi's semi-quantum nonlocal game.

Findings

Existence of shared entanglement is necessary and sufficient for positive payoff.

Constructed explicit examples demonstrating the game mechanics.

Established relations between the entanglement witness game and CHSH nonlocal game.

Abstract

Motivated by Buscemi's semi-quantum nonlocal game [PRL 108, 200401(2012)], We propose an entanglement witness game, a quantum game based on entanglement witness. Similar as the semi-quantum nonlocal game, the existence of entanglement shared by the players is necessary and sufficient for obtaining a positive average payoff in our entanglement witness game. Two explicit examples are constructed to demonstrate how to play our entanglement witness game and its relations with the CHSH nonlocal game.