Unitary Noise and the Mermin-GHZ Game

TL;DR

This paper examines how unitary noise affects the quantum advantage in the Mermin-GHZ pseudo-telepathy game, analyzing the threshold of noise levels where quantum strategies outperform classical ones.

Contribution

It introduces a model for pseudo-telepathy games and investigates the impact of unitary noise on quantum strategies in the Mermin-GHZ game, identifying noise thresholds for quantum advantage.

Findings

Quantum strategies remain superior up to a certain noise level.

Unitary noise can significantly degrade quantum advantage.

Thresholds for noise levels preserving quantum advantage are determined.

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.