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.
Quantum telepathy is the concept of using quantum entanglement to solve real-world problems involving decision coordination between parties with restricted communication. One possible reason for this restriction is a latency constraint: some pairs of parties do not have enough time to communicate with each other before they have to produce their outputs. Example scenarios include high frequency trading and distributed systems. Another reason is physical or operational isolation: for some pairs of parties, there is an obstacle to communication. Example scenarios include locating a stray traveler by a rescue team and coordination within a network where nodes are owned by competing firms. In this paper we give a concise overview of the different application areas of quantum telepathy. We find that these real-world problems can be modeled as a nonlocal game or its generalizations. We also discuss possible physical implementations. Quantum telepathy guarantees a quantum advantage via Bell's theorem and can directly solve real-world problems, such as reducing risk in high frequency trading or balancing data loads efficiently in ad hoc networks. Moreover, this quantum advantage can be physically realized with existing or near-term quantum hardware.