Probabilistic quantum teleportation of shared quantum secret

Very recently,Lee et al.proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network[Phys.Rev.Lett.124060501(2020)].This quantum network is encoded with a maximally entangled GHZ state.In this paper,we consider a partially entangled GHZ state as the entanglement channel,where it can achieve,probabilistically,unity fidelity transfer of the state.Two kinds of strategies are given.One arises when an auxiliary particle is introduced and a general evolution at any receiver's location is then adopted.The other one involves performing a single generalized Bell-state measurement at the location of any sender.This could allow the receivers to recover the transmitted state with a certain probability,in which only the local Pauli operators are performed,instead of introducing an auxiliary particle.In addition,the successful probability is provided,which is determined by the degree of entanglement of the partially multipartite entangled state.Moreover,the proposed protocol is robust against the bit and phase flip noise.