General criteria for certifying genuine high-dimensional quantum teleportation
Phys. Rev. Applied 26, 054002 – Published 2 November, 2026
DOI: https://doi.org/10.1103/scd3-z4gw
Abstract
Developing reliable methods for certifying the dimension of a given quantum system or process is essential to ensure the validity of the claimed realization of high-dimensional (HD) quantum advantages. The existing criteria for certifying genuine HD quantum teleportation (HDQT) mainly focus on demonstrating the successful transmission of genuine HD quantum states. However, a complete certification of HDQT must also identify the entanglement dimension of the resource, which is critical for verifying whether the transmission capacity and noise resilience meet the necessary thresholds. Here, we propose two universal criteria (based on fidelity and robustness, respectively) for certifying genuine HDQT behaviors that can close this gap by fully identifying the dimension of entanglement. Both criteria require only the input and output teleportation data and remain feasible under partial Bell-state measurements. Furthermore, the robustness-based criterion has stronger noise resistance and it requires no prior assumptions about local operations, making it robust even in black-box scenarios. Our results establish a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, pivotal for ensuring reliable links in HD quantum networks.
