Identifying genuine entanglement of lossy noisy very large scale continuous variable Greenberger-Horne-Zeilinger state

TL;DR

This paper introduces a general, efficient framework for detecting genuine entanglement in large-scale continuous variable quantum systems, applicable even under loss and noise conditions, with demonstrated results on massive multimode states.

Contribution

It presents a novel entanglement detection method based on uncertainty relations and sign matrix techniques, capable of handling very large systems and various entanglement structures.

Findings

Applicable to systems with over a hundred million modes

Effective under photon loss and noise environments

Can identify genuine entanglement in large-scale CV GHZ states

Abstract

Genuine entanglement identification of large scale systems is crucial for quantum computation, quantum communication and quantum learning advantage. In contrast to experiments, where noisy intermediate-scale programmable photonic quantum processors have been developed, theoretically very limited results have been achieved for detecting genuine entanglement of continuous variable multipartite systems. We propose a quite general and efficient entanglement detection framework for all kinds of multipartite entanglement of continuous variable systems based on uncertainty relations and the sign matrix technique. Matrix criteria are demonstrated and can be applied to various entanglement depth and k-separability problems of multimode systems. We illustrate the genuine entanglement conditions of continuous variable Greenberger-Horne-Zeilinger states of more than a hundred million modes in a photon loss and noise environment.