General Criteria for Certifying Genuine High-Dimensional Quantum Teleportation

TL;DR

This paper introduces two universal criteria based on fidelity and robustness for certifying genuine high-dimensional quantum teleportation, fully identifying entanglement dimension with minimal assumptions.

Contribution

It proposes novel, practical criteria that can certify the entanglement dimension in high-dimensional quantum teleportation using only input-output data.

Findings

Both criteria require only input and output data.

The robustness-based criterion has stronger noise resistance.

Criteria are feasible under partial Bell-state measurements.

Abstract

Developing reliable methods for certifying the dimension of a given quantum system or process is essential to ensure the validity of 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 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 the 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 scenario. Our results establish a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, pivotal for ensuring the reliable links in HD quantum networks.