A Rational Hierarchical Quantum State Sharing Protocol

In this paper, we propose a rational hierarchical quantum state sharing protocol. First, the dealer shares an arbitrary two-particle entangled state with m high-power players and n low-power players through (m + n + 1)-particle cluster states. The high-power players and low-players have different authorities to reconstruct the quantum state. In detail, when a high-power player reconstructs the quantum state, he needs the help of the other high-power players and any low-power players; when a low-power player reconstructs the quantum, he needs the help of all the players. Then, in order to guarantee the fairness of the protocol, we make the players with different powers have the same possibility to be the player David who can reconstruct the quantum state shared by the dealer Alice, which means David is elected by all the rational players. Second, in the process of reconstructing the quantum state, when David is a high-power player, he does not need the help of all the low-power players. Under this circumstance, we analyze the game process and solve the bargaining equilibrium between David and the low-power players selected by David based on the Rubenstein bargaining model with incomplete information. Finally, our protocol achieves security, fairness, correctness, and strict Nash equilibrium, and conforms to the actual scenario.