Certifying Unknown Genuine Multipartite Entanglement by Neural Networks

TL;DR

This paper demonstrates that neural networks can effectively certify genuine multipartite entanglement in unknown quantum states using measurement data, offering a practical and robust approach for experimental quantum physics.

Contribution

It introduces a neural network-based method to certify multipartite entanglement from measurement data, including new results and efficiency improvements.

Findings

Neural networks accurately certify genuine multipartite entanglement.

The method is robust against measurement device flaws.

Efficiency can be improved by feature size reduction.

Abstract

Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already NP-Hard to determine whether it is entangled or not. Therefore, it is hard to efficiently solve the above problem generally. However, since genuine multipartite entanglement is such a fundamental concept that plays a crucial role in many-body physics and quantum information processing tasks, finding realistic approaches to certify genuine multipartite entanglement is undoubtedly necessary. In this work, we show that neural networks can provide a nice solution to this problem, where measurement statistics data produced by measuring involved quantum states with local measurement devices serve as input features of neural networks. By testing our models on many specific multipartite quantum states, we show that they can certify genuine multipartite entanglement very accurately, which even include some new results unknown before. We also exhibit a possible way to improve the efficiency of our models by reducing the size of features. Lastly, we show that our models enjoy remarkable robustness against flaws in measurement devices, implying that they are very experiment-friendly.