Quantifying high-dimensional entanglement via classes of symmetric measurements
Phys. Rev. A 113, 022440 – Published 23 February, 2026
DOI: https://doi.org/10.1103/753k-qwf4
Abstract
High-dimensional entanglement is a cornerstone of quantum information science, yet its characterization remains hindered by resource-intensive tomography and fragmented detection frameworks. In this work we propose an entanglement criterion from mutually unbiased equiangular tight frames, which integrates and extends existing approaches grounded in mutually unbiased bases and equiangular measurements [Morelli et al., Phys. Rev. Lett. 131, 170201 (2023)]. This criterion provides rigorous quantitative links to key entanglement properties, facilitating both qualitative evaluation of the Schmidt number and quantitative estimation of entanglement fidelity. Notably, it requires significantly fewer global projections compared to full tomography, thereby substantially lowering the experimental complexity in high-dimensional systems. Evaluated under realistic depolarizing and dephasing noise scenarios, the proposed method demonstrates an advantageous balance between measurement efficiency and robustness to noise, outperforming prior approaches. Therefore, this criterion may serve as a unified analytical framework for quantifying entanglement in complex quantum systems.
