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 $2\times3$. In this study, we use deep convolutional NNs, 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.

翻译：量子纠缠是各种量子信息协议与算法中常用的基本性质。然而，对于大于 $2\times3$ 的系统，纠缠识别问题至今仍未获得通用解。在本研究中，我们采用监督机器学习中的深度卷积神经网络，对三量子比特系统中任意二分划的量子纠缠进行识别。我们证明，即使训练数据不包含具有挑战性的部分转置正定纠缠态（PPTES）——这类态通常无法被识别（并正确标记），仅使用排除PPTES的随机密度矩阵合成数据集进行训练，所得模型对训练数据之外的PPTES态仍能表现出良好的准确度。我们的目标是提升模型对PPTES的泛化能力。通过采用半监督方式训练的孪生三重网络施加保持纠缠的对称操作，我们提高了模型的准确度及其识别PPTES的能力。此外，通过构建孪生模型集成，我们观察到更优的泛化性能，这类似于为不同类别的态寻找不同类型纠缠见证子的思想。