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.

翻译：我们构建了一种机器学习模型，利用以无监督方式在随机生成态上训练的神经网络，来探测三量子比特系统中的关联。该网络被迫识别可分离态，而关联态则被检测为异常。令人惊讶的是，我们发现所提出的检测器在区分量子关联的较弱形式——即量子失谐——时，其性能远优于对纠缠的区分。实际上，即使处于纠缠检测的最优阈值，该检测器也倾向于严重高估纠缠态集合，而对失谐态集合的低估程度则小得多。为说明被归类为量子关联态的性质，我们构建了一个包含各种类型态（纠缠态、可分离态，以及有失谐和无失谐态）的示意图。研究发现，识别损失的近零值能以高精度复现无失谐可分离态的形状，尤其考虑到该集合在示意图上的非平凡形态。网络架构经过精心设计：它保持可分离性，且其输出在量子比特置换下具有等变性。我们证明，架构选择对获得最高检测精度至关重要，其性能远优于仅利用部分迹运算的基线模型。