Resource-Efficient Teleportation of High-Dimensional Quantum Coherence via Initial Phase Engineering

High-dimensional quantum systems leverage an expanded Hilbert space to enhance resilience against decoherence and noise. However, standard quantum teleportation is fundamentally limited by the quadratic growth of measurement complexity and high classical communication overhead, requiring the resolution of $d^2$ Bell states and $2\log_2 d$ classical bits. In this study, we propose a resource-efficient high-dimensional coherence teleportation (REHDCT) protocol. By designing $d$ sets of specialized positive operator-valued measure (POVM) bases, our protocol achieves a 50\% reduction in classical communication by utilizing one of the $d$ designed POVM sets, which effectively scales the measurement complexity from $O(d^2)$ to $O(d)$. Furthermore, we demonstrate that by utilizing initial phase engineering to align the target qudit with the measurement basis, theoretically perfect teleportation of quantum coherence can be achieved for arbitrary qudit states. A quantitative robustness analysis reveals that the protocol remains highly resilient to operational errors, maintaining an efficiency above 99.6\% even under a 0.1 rad phase deviation for $d=16$. Our analysis under various noise models (amplitude damping, phase flip, depolarizing, and dit-flip) confirms that high-dimensional systems exhibit an expanding quantum advantage window as dimensionality increases. Notably, under dit-flip noise, perfect coherence teleportation can be restored through the optimal selection of the POVM basis. These findings establish REHDCT as a practical, hardware-friendly framework for resource-efficient quantum communication in future high-dimensional networks.