Key Distribution based on Three Player Quantum Games

We study a new QKD that is different from the scheme proposed by \cite{Ramz2}, though it essentially takes our ground on three-player quantum games and Greenberg-Horne-Zeilinger triplet entangled state (GHZ state) \cite{Gree} is used. In the scheme proposed in this paper, players in the game, Bob and Charlie (and Alice also) can get some common key or information (applied strategies and their payoffs in the game), when Alice informs Bob and Charlie about some results of the measurement made by her. Even if somebody else knows the public information, he/she can not get any key information. There is not any arbiter in our scheme, since existence of an arbiter increases the risk of wiretapping. Lastly we discuss robustness of the proposed QKD method for eavesdrop. We show that though maximally entangled case and non-entangled case essentially provide an equivalent way as QKD, the latter is not available in the case where there are some eavesdroppers. At the same time, we point put that the entanglement of the initial state is crucial when a partially entangled state is used.