A quantum secret-sharing protocol with fairness

A quantum secret-sharing (QSS) protocol consists of two main phases, called sharing and reconstruction. In the first phase, the dealer selects a secret, divides it into several shares, and sends each participant its share securely with a quantum channel. In the second phase, the participants run an interactive protocol in order to reconstruct the secret. If the participants can communicate via a broadcast channel, they can show their shares and learn the secrets simultaneously. So what happens if the channel is not simultaneous? In this paper, we propose a QSS protocol with cheaters by using partially and maximally entangled states. A secure and fair reconstruction mechanism is designed, in a way that each participant can learn or cannot learn the secret simultaneously.