Conclusive Multiparty Joint Remote Preparation of an Arbitrary Single-particle State in Amplitude-damping Channel

In the present article, two conclusive multiparty quantum state preparation (JRSP) schemes in the amplitude damping channel are proposed, which respectively prepare an arbitrary single-qubit state and single-qutrit state. To achieve this, the detailed procedures of using entanglement compensation in an amplitude-damped channel to share pure entangled quantum states are first proposed. Then, using the pure entangled quantum state shared between the two senders and their two agents as a quantum channel, the senders’ original state, i.e., a single-qubit state (or single-qutrit state) is prepared at one of the locations where the two distant agents are located in this way that both senders perform single-qubit projective measurements (or one sender performs a single-qutrit positive operator-valued measurement while the other performs a single-qutrit projective measurement) based on their understanding of the original state, and the original single-qubit (or single-qutrit) state can be probabilistically reconstructed under two agents collaborating together. Subsequently, the above two schemes are generalized from 2 agents to the scenario of n (\( n \ge 3 \)) agents. In addition, through the analysis, we can see that the above two basic schemes can also be generalized from 2 senders to the scenario of m (\( m \ge 3 \)) senders.