Verifying Genuine High-Order Entanglement

TL;DR

This paper presents an efficient scheme for verifying genuine high-order entanglement in complex multipartite multilevel quantum systems, significantly reducing measurement requirements for experimental validation.

Contribution

It introduces a universal detection method for high-order entanglement that requires only two local measurements per degree of freedom, regardless of system complexity.

Findings

Enables detection of states close to qudit Bell, GHZ, and cluster states

Reduces measurement overhead in entanglement verification

Facilitates experimental implementation of complex entangled states

Abstract

High-order entanglement embedded in multipartite multilevel quantum systems (qudits) with many degrees of freedom (DOFs) plays an important role in quantum foundation and quantum engineering. Verifying high-order entanglement without the restriction of system complexity is a critical need in any experiments on general entanglement. Here, we introduce a scheme to efficiently detect genuine high-order entanglement, such as states close to genuine qudit Bell, Greenberger-Horne-Zeilinger, and cluster states as well as multilevel multi-DOF hyperentanglement. All of them can be identified with two local measurement settings per DOF regardless of the qudit or DOF number. The proposed verifications together with further utilities such as fidelity estimation could pave the way for experiments by reducing dramatically the measurement overhead.