Efficient certification of high-dimensional entanglement
Phys. Rev. A 113, 022429 – Published 18 February, 2026
DOI: https://doi.org/10.1103/wfqb-rfl9
Abstract
High-dimensional entanglement (HDE) is a valuable resource in quantum information processing, and efficient certification of HDE is crucial to many applications. In this work, we propose a simple and general framework for certifying HDE in general bipartite pure states under restricted operations, such as local operations and classical communication (LOCC). On this basis, we show that HDE in general bipartite pure states can be certified efficiently. Moreover, the sample cost required to certify a given degree of HDE even decreases monotonically with the local dimensions. In addition, for a general two-qubit pure state, we construct an optimal entanglement certification strategy based on separable operations, which can be realized by LOCC when the target state has sufficiently high entanglement. The core concept of our framework is versatile and can be extended to certify a wide range of critical quantum resources under restricted operations.
