Efficient certification of high-dimensional entanglement

TL;DR

This paper introduces a simple, efficient framework for certifying high-dimensional entanglement in bipartite pure states, reducing sample costs and enabling practical verification under restricted operations like LOCC.

Contribution

The work presents a general certification framework for high-dimensional entanglement that is efficient and adaptable, including an optimal strategy for two-qubit states using separable operations.

Findings

Sample cost decreases with local dimensions.

Efficient certification under LOCC for high-dimensional states.

Optimal strategy for two-qubit entanglement verification.

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 for certifying 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 resources under restricted operations.