Quantifying Unknown Entanglement by Neural Networks

TL;DR

This paper demonstrates that neural networks can effectively quantify unknown quantum entanglement from measurement data, outperforming previous methods and revealing a correlation with quantum nonlocality.

Contribution

The authors introduce a neural network approach to quantify entanglement using measurement outcomes, achieving superior accuracy and range over existing semi-device-independent protocols.

Findings

Neural networks accurately quantify bipartite and multipartite entanglement.

Performance improves on states with stronger quantum nonlocality.

Outperforms previous semi-device-independent methods in precision and applicability.

Abstract

Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by any observables directly. In this paper, we train neural networks to quantify unknown entanglement, where the input features of neural networks are the outcome statistics data produced by locally measuring target quantum states, and the training labels are well-chosen quantities. For bipartite quantum states, this quantity is coherent information, which is a lower bound for the entanglement of formation and the entanglement of distillation. For multipartite quantum states, we choose this quantity as the geometric measure of entanglement. It turns out that the neural networks we train have very good performance in quantifying unknown quantum states, and can beat previous approaches like semi-device-independent protocols for this problem easily in both precision and application range. We also observe a surprising phenomenon that on quantum states with stronger quantum nonlocality, the neural networks tend to have better performance, though we do not provide them any knowledge on quantum nonlocality.