Detecting high-dimensional multipartite entanglement via some classes of measurements

TL;DR

This paper develops new criteria based on specific quantum measurements to detect high-dimensional multipartite entanglement efficiently, surpassing previous methods and enabling experimental detection without full state tomography.

Contribution

The authors introduce novel entanglement detection criteria using mutually unbiased bases, measurements, and SIC measurements applicable to high-dimensional and heterogeneous multipartite systems.

Findings

Criteria can detect $k$-nonseparability in multipartite qudit systems

Methods are more efficient and broadly applicable than previous ones

Enable entanglement detection without full quantum state tomography

Abstract

Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite systems of subsystems with different dimensions. It is proved that these criteria can detect the $k$-nonseparability ($k$ is even) of multipartite qudit systems and arbitrary high dimensional multipartite systems of $m$ subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography.