Memory and correlation impacts in 3D-Pauli-like noisy channels for controlled teleportation of arbitrary single-qutrit states

Abstract The purpose of this paper is to further investigate the correlated and memory effects in 3D-Pauli-like noisy channels for controlled teleportation of an arbitrary unknown single-qutrit state. We first construct a three-qutrit maximally entangled state in a three-dimensional (3D) Hilbert space and subsequently propose a 3D controlled quantum teleportation (CQT) scheme for an arbitrary unknown single-qutrit state using the constructed three-qutrit maximally entangled state as the quantum channel. In this ideal case, through a few simple 3D unitary operations, the two communicating parties can perfectly accomplish the teleportation task under the supervision of the controller. Subsequently, we examine the performance of this CQT scheme under two successive uses of a 3D-Pauli-like noisy channel with memory, where the noise errors are categorized into four types: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. For each noise type, an analytical expression of the average fidelity is derived as a function of both the noise and memory parameters. Specifically, we find that, regardless of the noise strength, memory enhances the average fidelity for trit-flip and t-depolarizing noises, whereas for t-phase-flip and trit-phase-flip noises, memory reduces the average fidelity once the noise intensity exceeds a certain threshold. This indicates that in the first two noisy channels, memory can improve the communication efficiency of CQT, while in the latter two, excessive noise causes memory to diminish the teleportation performance.