Maximally entangled state in pseudo-telepathy games

Abstract

A pseudo-telepathy game is a non-local game which can be won with probability one using quantum strategies but not using classical ones. Our central question is whether there exist two-party pseudo-telepathy games which cannot be won with probability one using a maximally entangled state. Towards answering this question, we develop conditions under which maximally entangled state suffices. Our main result shows that for any game G, there exists a game ˜G such that G admits a perfect strategy using a maximally entangled state if and only if ˜G admits some perfect finite-dimensional quantum strategy.