Quantum entanglement is a fundamental property commonly used in various quantum information protocols and algorithms. Nonetheless, the problem of identifying entanglement has still not reached a general solution for systems larger than two qubits. In this study, we use deep convolutional neural networks, a type of supervised machine learning, to identify quantum entanglement for any bipartition in a 3-qubit system. We demonstrate that training the model on synthetically generated datasets of random density matrices excluding challenging positive-under-partial-transposition entangled states (PPTES), which cannot be identified (and correctly labeled) in general, leads to good model accuracy even for PPTES states, that were outside the training data. Our aim is to enhance the model's generalization on PPTES. By applying entanglement-preserving symmetry operations through a triple Siamese network trained in a semi-supervised manner, we improve the model's accuracy and ability to recognize PPTES. Moreover, by constructing an ensemble of Siamese models, even better generalization is observed, in analogy with the idea of finding separate types of entanglement witnesses for different classes of states. The neural models' code and training schemes, as well as data generation procedures, are available at github.com/Maticraft/quantum_correlations.

翻译：量子纠缠是各类量子信息协议与算法中常用的基本性质。然而，对于大于两量子比特的系统，纠缠识别问题尚未得到通用解决方案。本研究采用深度卷积神经网络（一种监督式机器学习方法）来识别三量子比特系统中任意二分划的量子纠缠。我们证明，在排除通常无法普遍识别（及正确标注）的困难正定部分转置纠缠态（PPTES）后，使用随机密度矩阵合成数据集训练的模型，即使对训练数据之外的PPTES态也能保持良好的准确率。本研究旨在增强模型对PPTES的泛化能力。通过半监督方式训练三重孪生网络施加纠缠保持对称操作，我们提升了模型对PPTES的识别精度与能力。此外，构建孪生模型集成后观察到更优泛化性能，这与针对不同类别态寻找不同类型纠缠见证的思路相类似。神经模型的代码、训练方案及数据生成流程均发布于github.com/Maticraft/quantum_correlations。