Enhanced high-dimensional teleportation in correlated amplitude damping noise by weak measurement and environment-assisted measurement

High-dimensional teleportation provides various benefits in quantum networks and repeaters, but all these advantages rely on the high-quality distribution of high-dimensional entanglement over a noisy channel. It is essential to consider correlation effects when two entangled qutrits travel sequentially through the same channel. In this paper, we present two strategies for enhancing qutrit teleportation in correlated amplitude damping (CAD) noise by weak measurement (WM) and environment-assisted measurement (EAM). The fidelity of both approaches has been dramatically improved due to the probabilistic nature of WM and EAM. We have observed that the correlation effects of CAD noise result in an increase in the probability of success. A comparison has demonstrated that the EAM scheme usually outperforms the WM scheme in regard to fidelity. Our research expands the capabilities of WM and EAM as quantum techniques to combat CAD noise in qutrit teleportation, facilitating the development of advanced quantum technologies in high-dimensional systems.