Fault-Tolerate Three-Party Quantum Secret Sharing over a Collective-Noise Channel

We present a fault-tolerate three-party quantum secret sharing (QSS) scheme over a collective-noise channel. Decoherence-free subspaces are used to tolerate two noise modes, a collective-dephasing channel and a collective-rotating channel, respectively. In this scheme, the boss uses two physical qubits to construct a logical qubit which acts as a quantum channel to transmit one bit information to her two agents. The agents can get the information of the private key established by the boss only if they collaborate. The boss Alice encodes information with two unitary operations. Only single-photon measurements are required to rebuilt Alice's information and detect the security by the agents Bob and Charlie, not Bell-state measurements. Moreover, Almost all of the photons are used to distribute information, and its success efficiency approaches 100% in theory.