Asymmetric controlled remote implementation of operations in different dimensions

Quantum entanglement is essential for the realization of distributed computing and has been implemented in various types of two-level systems. However, high-dimensional quantum protocols are rarely investigated both theoretically and experimentally, despite the remarkable advantages that high-dimensional quantum systems exhibit over two-level systems for certain quantum information and computing tasks. Here, we propose asymmetric protocols that utilize different dimensional systems to prepare the stator and achieve remote state operations with the assistance of shared N-partite graph states. Our protocols demonstrate convincing control power and security, with all implementations achievable through local operations and classical communications. The experimental realization of high-dimensional quantum systems and operations is presented using current technology. Our work contributes towards achieving arbitrary high-dimensional quantum protocols and paves the way for implementing high-dimensional quantum communication and computation.