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Quantum refereed game


Quantum refereed game in quantum information processing is a class of games in the general theory of quantum games. It is played between two players, Alice and Bob, and arbitrated by a referee. The referee outputs the pay-off for the players after interacting with them for a fixed number of rounds, while exchanging quantum information.

An -turn quantum referee performs rounds of interaction with the player Alice and Bob. Each interaction involves receiving some quantum states from Alice and Bob, processing the quantum states together with the "left-over" state from the previous interaction, producing some output state, and sending part of the output state to the players. At the end of the rounds, the referee processes the final state received from the players and decides the pay-off for Alice and Bob.

Mathematically, an n-turn referee is a measuring co-strategy whose input spaces and output spaces are of the form


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