Quantum Prisoners' Dilemma under Enhanced Interrogation

TL;DR

This paper explores how tripartite entanglement in a quantum prisoners' dilemma can lead to Nash equilibria that align with cooperative Pareto optimality, revealing complex strategic structures.

Contribution

It introduces a third qubit to enlarge the Hilbert space, enabling analysis of tripartite entanglement's impact on game equilibria and cooperation.

Findings

Nash equilibria can match Pareto optimal cooperation with tripartite entanglement.

Game structure varies significantly between W-state and bipartite entanglement.

Tripartite entanglement influences strategic outcomes in quantum games.

Abstract

In the quantum version of prisoners' dilemma, each prisoner is equipped with a single qubit that the interrogator can entangle. We enlarge the available Hilbert space by introducing a third qubit that the interrogator can entangle with the other two. We discuss an enhanced interrogation technique based on tripartite entanglement and analyze Nash equilibria. We show that for tripartite entanglement approaching a W-state, there exist Nash equilibria that coincide with the Pareto optimal choice where both prisoners cooperate. Upon continuous variation between a W-state and a pure bipartite entangled state, the game is shown to have a surprisingly rich structure. The role of bipartite and tripartite entanglement is explored to explain that structure.