Unitary Noise and the Mermin-GHZ Game

Abstract: Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.