Abstract Generalization is essential for reliable machine-learning detection of quantum steerability. In this work, we develop a CNN-based approach using the matrix versions of the full-information feature F 1 and the steering-determined feature F 2 as inputs for two-qubit steerability classification. Several physically distinct state families with reliable labels are employed to evaluate classifier generalization. Vector-input classifiers based on F 1 and F 2 are included as benchmarks under a unified classification protocol. Across the considered classifiers and test datasets, F 2 -based models exhibit consistently more stable generalization than their F 1 -based counterparts, indicating that steering-determined feature extraction plays a more dominant role than classifier selection in the observed performance improvement in the considered settings. Meanwhile, no single classifier is uniformly optimal across all physical state families. Since CNN– F 2 achieves the best overall performance on the T -diagonal benchmarks, it is further employed to visualize and estimate the projective-measurement steering hierarchy of axially symmetric states, a special subclass of T -diagonal states.
Abstract Generalization is essential for reliable machine-learning detection of quantum steerability. In this work, we develop a CNN-based approach using the matrix versions of the full-information feature F 1 and the steering-determined feature F 2 as inputs for two-qubit steerability classification. Several physically distinct state families with reliable labels are employed to evaluate classifier generalization. Vector-input classifiers based on F 1 and F 2 are included as benchmarks under a unified classification protocol. Across the considered classifiers and test datasets, F 2 -based models exhibit consistently more stable generalization than their F 1 -based counterparts, indicating that steering-determined feature extraction plays a more dominant role than classifier selection in the observed performance improvement in the considered settings. Meanwhile, no single classifier is uniformly optimal across all physical state families. Since CNN– F 2 achieves the best overall performance on the T -diagonal benchmarks, it is further employed to visualize and estimate the projective-measurement steering hierarchy of axially symmetric states, a special subclass of T -diagonal states.
Generalization ability is essential for assessing the robustness of quantum steerability classifiers. In this work, we investigate robust steerability classification from the perspective of key feature extraction and matrix structure preservation. The dataset introduced in Phys. Rev. A 100, 022314 (2019) provides the training basis for the present work. With strictly unsteerable random states, T-diagonal states, and All-Versus-Nothing (AVN) states, we evaluate the generalization performance of support vector machines (SVMs), multilayer perceptrons (MLPs), and deep perceptron control classifiers(DPs) trained on full-information features. None of these classifiers perform consistently on T-diagonal or AVN states. Given that stochastic local operations and classical communication and local unitary transformations preserve steerability, we introduce a key feature that determines steerability. SVMs trained on this feature overcome the instability on T-diagonal states but still fail on AVN states. Moreover, this feature alone is insufficient for training robust neural-network-based steerability classifiers. Recognizing that flattening quantum states into one-dimensional vectors may destroy their intrinsic matrix structure, we introduce matrix versions of both features and train convolutional neural networks on them. The most robust overall performance among the tested classifiers is achieved only when the matrix structure is preserved and key features are extracted simultaneously. Finally, as an application, we employ the most robust classifiers to predict the number of projective measurements required to detect the steerability of axially symmetric states
Only a few states in high-dimensional systems can be identified as (un)steerable using existing theoretical or experimental methods. We utilize semidefinite programming (SDP) to construct a dataset for steerability detection in qutrit-qutrit systems. For the full-information feature F1, artificial neural networks achieve high classification accuracy and generalization, and perform better than the support vector machine. As feature engineering plays a pivotal role, we introduce a steering ellipsoidlike feature, F2, which significantly enhances the performance of each of our models. To address quantum steering detection in isotropic states, partially entangled states, and random states, we explore, respectively, the most tailored feature and classifier. Given that the SDP method provides only a sufficient condition for steerability detection, we establish the first rigorously constructed, accurately labeled dataset based on theoretical foundations. This dataset enables models to exhibit outstanding accuracy and generalization capabilities, independent of the choice of features. As applications, we investigate the steerability boundaries of isotropic states and partially entangled states, discover new steerable states, and determine their parameter ranges. This work not only advances the application of machine learning for probing quantum steerability in high-dimensional systems but also deepens the theoretical understanding of quantum steerability itself.
We use an error backpropagation (BP) neural network to determine whether an arbitrary two-qubit quantum state is steerable and optimize the steerability bounds of the generalized Werner state. Results show that, regardless of how we select the features for the quantum states, we can use the BP neural network to construct several models to obtain high-performance quantum steering classifiers compared with the support vector machine. Moreover, we predict the steerability bounds of the generalized Werner states using the classifiers that are newly constructed by the BP neural network; that is, the predicted steerability bounds are closer to the theoretical bounds. In particular, high-performance quantum steering classifiers with partial information about the quantum states that we need to measure in only three fixed measurement directions are obtained.
Abstract Quantum steering is an important form of nonclassical correlation and plays a central role in one-sided device-independent quantum information processing. However, efficiently determining whether an arbitrary two-qubit state is steerable remains challenging, since semidefinite-programming-based certification generally depends on the choice of measurement settings and can become computationally demanding. In this work, we propose an interpretable quantum steering detection scheme based on Kolmogorov–Arnold Networks (KANs). The training labels are generated through semidefinite programming for randomly sampled two-qubit density matrices. Several physically motivated feature representations are constructed to investigate the influence of measurement and feature reduction. Owing to their learnable univariate edge functions and symbolic formula extraction capability, KANs provide not only accurate classification but also a more transparent representation of the learned steering decision boundary. Numerical experiments show that the proposed KAN-based classifiers can distinguish states with SDP-detected steering from states for which no witness is found under the sampled measurements. In particular, canonical-correlation features provide an effective representation for learning the steering boundary, and further feature compression can still retain competitive detection performance. These results indicate that KANs offer a promising, efficient, and interpretable machine-learning approach for finite-measurement steering detection of arbitrary two-qubit states.
Abstract 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.
In this paper, we establish an aggregate class distribution neural network (AGGNN) structure to determine whether an arbitrary two-qubit quantum state is steerable. Compared to the classification results obtained using a support vector machine (SVM) and a backpropagation neural network (BPNN), we obtain higher-accuracy quantum-steering classification models via the AGGNN, as well as steerability bounds of generalized Werner states, which are more similar to the theoretical bounds. In particular, when we only know partial information about the quantum states, higher-performance quantum-steering classifiers are obtained compared to those via SVM and BPNN.