Separation between Classical and Quantum Winning Strategies for the Matching Game

TL;DR

This paper explores the separation between classical and quantum strategies in the matching game, a pseudo-telepathy game, by analyzing input sizes where quantum strategies outperform classical ones.

Contribution

It introduces a general model for pseudo-telepathy games and investigates the minimal input size for the matching game to exhibit quantum advantage.

Findings

Quantum strategies can eliminate communication in the matching game.

The minimal input size for quantum advantage is characterized.

Classical strategies require communication, unlike quantum strategies.

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. The matching game is the newest member of the family of pseudo-telepathy games. After introducing a general model for pseudo-telepathy games, we focus on the question what the smallest size of inputs is for which the matching game is a pseudo-telepathy game.