Four-Qubit CHSH Games

TL;DR

This paper extends the CHSH quantum game to four players, identifying new quantum games that demonstrate significant advantages using GHZ and W states, and verifies these results on an online quantum computer.

Contribution

It introduces two new four-player quantum games with notable quantum advantages and experimentally verifies these advantages using online quantum computing.

Findings

GHZ state yields a 22.5% quantum advantage in the new game.

W state provides an even greater quantum advantage.

Experimental validation confirms the theoretical quantum benefits.

Abstract

In this paper, the CHSH quantum game is extended to four players. This is achieved by exploring all possible 4-variable Boolean functions to identify those that yield a game scenario with a quantum advantage using a specific entangled state. Notably, two new four-player quantum games are presented. In one game, the optimal quantum strategy is achieved when players share a $GHZ$-state, breaking the traditional 10\% gain observed in 2 and 3 qubit CHSH games and achieving a 22.5\% gap. In the other game, players gain a greater advantage using a $W$-state as their quantum resource. Quantum games with other four-qubit entangled states are also explored. To demonstrate the results, these game scenarios are implemented on an online quantum computer, and the advantage of the respective quantum resource for each game is experimentally verified.