Conclusive multiparty quantum state sharing in amplitude-damping channel

In this paper, two conclusive multiparty quantum state sharing protocols in amplitude damping channel are proposed that, respectively share an arbitrary unknown single-qubit state and single-qutrit state. To achieve this aim, the detailed processes of sharing pure entangled quantum states as quantum channel in amplitude damping channel via entanglement compensation is proposed first. Then, based on the pure entangled quantum state shared among dealer and all agents, the dealer’s secret quantum information, i.e., single-qubit state (or single-qutrit state) is split in such a way that it can be probabilistically reconstructed through introducing an auxiliary qubit (or qutrit) and performing appropriate operations provided that all the receivers collaborate together. Through the analysis, we have found that whether in single-qubit or single-qutrit state sharing protocols, the successful probability of receiver recovering the secret quantum information is only determined by the small one among the absolute values of the coefficients characterizing the quantum channel. In addition, through the analysis, it proves that the conclusive multiparty single-qutrit state sharing has higher efficiency than single-qubit state sharing under the same amplitude damping strength.