Fault tolerant quantum secret sharing against collective- amplitude-damping noise

We present a quantum secret sharing protocol against collective-amplitude-damping noise. Each logical qubit is encoded in two qubit noiseless states. So it can function over such a noisy channel. The two agents encode their messages on each logical qubit only by performing a permutation operation on two physical qubits. Although each logical qubit received by each agent only carries a bit of information, the boss Alice can read out her agents＇ information by discriminating two orthogonal states by performing single-qubit measurements assisted by local operation and classical communication （LOCC）.