Learning the hierarchy of steering measurement settings of qubit-pair states with kernel-based quantum models

Quantum steering has been proven to be a unique quantum correlation sandwiched between Bell nonlocality and quantum entanglement. Due to its fundamental importance, quantum steering has been studied extensively. To demonstrate steerability, one relies on a particular resource referred to as steerable assemble on one side of a two-party system. However, it is generically unclear how to reach such steerable resource from a bipartite quantum state. For this purpose, one must optimize over all possible measurement settings, which constitute a hierarchical structure. On the other hand, in light of the rapid development of quantum computing technology, quantum machine learning (QML) has emerged as a field with a promising potential in demonstrating quantum advantage. Here we leverage the power of kernel-based QML models to infer the hierarchy of steering measurement settings. By using a computational protocol, we can generate an appropriate dataset necessary for training the models. Additionally, based on the physics of quantum steering, we encode the states to be recognized into five different types of features. This helps us identify the most compact characterization of Alice-to-Bob steerability, which is Alice’s regularly aligned steering ellipsoid. We then apply the well-trained models to predict the hierarchy for three specific families of states. We also compare the QML model with two classical models, demonstrating its superior performance, as well as the practical quantum advantage.