Characterizing high-dimensional multipartite entanglement beyond Greenberger-Horne-Zeilinger fidelities

TL;DR

This paper introduces a new method for certifying high-dimensional multipartite entanglement that surpasses traditional fidelity-based witnesses, using simple measurements and applicable to noisy and random states.

Contribution

The authors develop a novel certification technique that effectively detects high-dimensional multipartite entanglement without complex measurements, improving over existing methods.

Findings

Method outperforms traditional GHZ fidelity witnesses

Effective on noisy and random high-dimensional states

Simpler to evaluate than existing criteria

Abstract

Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the particles have many accessible levels, i.e., they are of high dimension, which leads to a potentially high-dimensional multipartite entangled state. These are important resources for an ever-increasing number of tasks, especially when a network of parties needs to share highly entangled states, e.g., for communicating more efficiently and securely. For these applications, as well as for purely theoretical arguments, it is important to be able to certify both the high-dimensional and the genuine multipartite nature of entangled states, possibly based on simple measurements. Here we derive a novel method that achieves this and improves over typical entanglement witnesses like the fidelity with respect to states of a Greenberger-Horne-Zeilinger (GHZ) form, without needing more complex measurements. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect GHZ states with random noise, as well as on purely randomly chosen ones and find that, in comparison with other available criteria our method provides a significant advantage and is often also simpler to evaluate.