Quantifying Quantum Steerability of Qubit-Pair States via Hybrid Quantum-Classical Machine Learning Framework

Quantum steering has been recognized as a distinct form of quantum correlation that lies between quantum entanglement and Bell nonlocality. It has gained significant attention in recent years due to its fundamental importance and diverse applications in quantum information science. In general, the quantification of quantum steerability relies on semidefinite programming (SDP) analysis of Bob’s assemblage. In contrast, our approach operates directly on the quantum state by optimizing Alice’s measurement observables. This procedure involves the optimization over all possible measurement settings, resulting in substantial computational overhead. Moreover, the implementation of SDP requires complete knowledge of the quantum state, which in turn necessitates quantum state tomography—an experimentally demanding and resource-intensive process.

In this study, we employ a Hybrid Quantum-Classical Machine Learning (HQCML) model to estimate the steerable weight of qubit-pair systems under specific measurement settings. To overcome the computational challenges associated with the optimization process, we develop a computational protocol based on iterative testing, which generates the necessary data to training the models.

Additionally, without relying on extensive quantum state tomography, our method enables the quantification of quantum steerability directly from physically meaningful features. Based on the physics of quantum steering, we encode the quantum states to be recognized into five distinct feature types. This feature design allows the model to capture the most compact characterization of Alice-to-Bob steerability, represented by Alice’s regularly aligned steering ellipsoid. In comparison with purely classical models, the proposed HQML framework requires significantly fewer parameters than Artificial Neural Network (ANN), leading to improved resource efficiency and robust generalization capability.