Data-driven criteria for quantum correlations

TL;DR

This paper presents a machine learning approach using neural networks to detect quantum correlations in three-qubit systems, revealing better detection of quantum discord than entanglement and emphasizing the importance of architecture design.

Contribution

The study introduces an unsupervised neural network model that effectively detects quantum correlations, especially quantum discord, and highlights the significance of architecture in quantum state classification.

Findings

The model detects quantum discord more accurately than entanglement.

It overestimates entanglement but underestimates discordant states.

The architecture preserves separability and is permutation-equivariant.

Abstract

We build a machine learning model to detect correlations in a three-qubit system using a neural network trained in an unsupervised manner on randomly generated states. The network is forced to recognize separable states, and correlated states are detected as anomalies. Quite surprisingly, we find that the proposed detector performs much better at distinguishing a weaker form of quantum correlations, namely, the quantum discord, than entanglement. In fact, it has a tendency to grossly overestimate the set of entangled states even at the optimal threshold for entanglement detection, while it underestimates the set of discordant states to a much lesser extent. In order to illustrate the nature of states classified as quantum-correlated, we construct a diagram containing various types of states -- entangled, as well as separable, both discordant and non-discordant. We find that the near-zero value of the recognition loss reproduces the shape of the non-discordant separable states with high accuracy, especially considering the non-trivial shape of this set on the diagram. The network architecture is designed carefully: it preserves separability, and its output is equivariant with respect to qubit permutations. We show that the choice of architecture is important to get the highest detection accuracy, much better than for a baseline model that just utilizes a partial trace operation.