Parallel approximation of non-interactive zero-sum quantum games

TL;DR

This paper introduces an efficient parallel algorithm to approximate equilibria in non-interactive zero-sum quantum games, enabling polynomial-space simulation of one-turn quantum refereed games.

Contribution

It presents the first polynomial-space algorithm for approximating equilibria in a class of quantum games, advancing computational methods in quantum game theory.

Findings

Equilibrium points can be approximated efficiently in parallel.

One-turn quantum refereed games are simulatable in polynomial space.

The approach bridges quantum game theory and computational complexity.

Abstract

This paper studies a simple class of zero-sum games played by two competing quantum players: each player sends a mixed quantum state to a referee, who performs a joint measurement on the two states to determine the players' payoffs. We prove that an equilibrium point of any such game can be approximated by means of an efficient parallel algorithm, which implies that one-turn quantum refereed games, wherein the referee is specified by a quantum circuit, can be simulated in polynomial space.