Multi-party three-dimensional asymmetric cyclic controlled quantum teleportation in noisy environment

In this paper, a new scheme for asymmetric cyclic controlled teleportation of arbitrary three-dimensional unknown quantum states is proposed by performing three-dimensional Bell-state measurements and three-dimensional Hadamard transformation. The entangled state of thirteen-qutrit acts as the quantum channel to connect senders and receivers, which is constructed by a three-qutrit entangled state and five two-qutrit entangled states. In this scheme, Alice wants to transmit an arbitrary unknown single-qutrit state to Bob, at the same time, Bob wants to transmit an arbitrary unknown two-qutrit entangled state to Charlie and Charlie wants to transmit an arbitrary unknown three-qutrit entangled state to Alice under the control of the supervisor David. Participants can reconstruct the original states and make the scheme perfectly by performing appropriate unitary operation. Then, the scheme can be generalized to realize the asymmetric cyclic controlled quantum teleportation of N (N > 3) participants in the three-dimensional system, and come up with two universal schemes are determined by the parity of the participant. Furthermore, the scheme is investigated in two different noisy channels: amplitude-damping noise and phase-damping noise, and calculated the fidelities of the output states. It is demonstrated that the fidelities only depend on the coefficients of the initial state and the decoherence noisy rate. The security of the scheme is briefly analyzed and compares with the previous schemes in terms of efficiency. The proposed scheme contributes to advancing understanding of high-dimensional quantum teleportation.