Cyclic joint remote state preparation in noisy environment

We propose a scheme of cyclic joint remote state preparation for three sides, which takes advantage of three GHZ states to compose product state as quantum channel. Suppose there are six legitimate participants, says Alice, Bob, Charlie, David, Emma and Fred in the scheme. It can be shown that Alice and David can remotely prepare a single-qubit state on Bob’s side; meanwhile, Bob and Emma can remotely prepare a desired quantum state on Charlie’s side, and Charlie and Fred can also remotely prepare a single-qubit state on Alice’s side at the same time. Further, it can be achieved in the opposite direction of the cycle by changing the quantum channel. Based on it, we generalize this protocol to $$N (N\ge 3)$$N(N≥3) sides utilizing three multi-qubit GHZ-type states as quantum channel. Therefore, the scheme can achieve cyclic joint remote state preparation, which remotely prepares N states in quantum network with N-party, simultaneously. In addition, we consider that the effect of amplitude-damping noise of the initial states is prepared in four different laboratory. Clearly, we use fidelity to describe how much information has been lost in the cyclic process. Our investigation about the effect of noise shows that the preparing of the initial state in different laboratories will affect the loss of information.