Abstract Quantum steering has attracted increasing research attention because of its fundamental importance, as well as its applications in quantum information science. Here we leverage the power of the deep learning model to infer the steerability of quantum states with specific numbers of measurement settings, which form a hierarchical structure. A computational protocol consisting of iterative tests is constructed to overcome the optimization, meanwhile, generating the necessary training data. According to the responses of the well-trained models to the different physics-driven features encoding the states to be recognized, we can numerically conclude that the most compact characterization of the Alice-to-Bob steerability is Alice’s regularly aligned steering ellipsoid; whereas Bob’s ellipsoid is irrelevant. We have also provided an explanation to this result with the one-way stochastic local operations and classical communication. Additionally, our approach is versatile in revealing further insights into the hierarchical structure of quantum steering and detecting the hidden steerability.
Abstract Quantum steering has attracted increasing research attention because of its fundamental importance, as well as its applications in quantum information science. Here we leverage the power of the deep learning model to infer the steerability of quantum states with specific numbers of measurement settings, which form a hierarchical structure. A computational protocol consisting of iterative tests is constructed to overcome the optimization, meanwhile, generating the necessary training data. According to the responses of the well-trained models to the different physics-driven features encoding the states to be recognized, we can numerically conclude that the most compact characterization of the Alice-to-Bob steerability is Alice’s regularly aligned steering ellipsoid; whereas Bob’s ellipsoid is irrelevant. We have also provided an explanation to this result with the one-way stochastic local operations and classical communication. Additionally, our approach is versatile in revealing further insights into the hierarchical structure of quantum steering and detecting the hidden steerability.
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.
Quantum steering is an important nonclassical resource for quantum information processing. However, even though lots of steering criteria exist, it is still very difficult to efficiently determine whether an arbitrary two-qubit state shared by Alice and Bob is steerable or not, because the optimal measurement directions of Alice are unknown. In this work, we provide an efficient quantum steering detection scheme for an arbitrary two-qubit state with the help of machine learning, where Alice and Bob only need to measure in a few fixed measurement directions. In order to prove the validity of this method, we first realize a high-performance quantum steering classifier with the whole information. Furthermore, a high-performance quantum steering classifier with partial information is realized, where Alice and Bob only need to measure in three fixed measurement directions. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum steering via the machine learning approach.
Quantum steering exhibits an inherent asymmetric property that differs from both quantum entanglement and Bell nonlocality, which leads to no-way, one-way, and two-way steering. Flexibly manipulating the direction of quantum steering without reducing the quantum steerability is very important for information processing. In this paper, implementing sequential unsharp measurements and the steering-radius criterion, we show how to manipulate that steering direction among multiple Alices and Bobs. We demonstrate that the change in steering direction depends on the number of measurement settings and the sharpness of measurements. For a given two-qubit asymmetric state, we obtain 13 kinds of steering regions with different steering directions in the case of one Alice and three Bobs and obtain 11 kinds in the case with two Alices and two Bobs. For the case with one Alice and three Bobs, we further find a volume bound to visualize quantum steering. Our manipulation scheme is experimentally easy to achieve and rather assigns the steerability to more observers without reducing it, which offers a direct reference for the practical application of quantum steering.
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.
Not all entangled states can exhibit quantum steering, and determining whether a given entangled state is steerable is a crucial problem in quantum information theory. The main challenge lies in verifying the existence of a local hidden-state (LHS) model capable of reproducing all post-measurement assemblages generated by arbitrary measurements. To address this, we propose a machine learning-based framework that employs batch sampling of measurements and gradient-based optimization to construct an optimal LHS model. We validate our method by analyzing the steerability of two-qubit Werner and two-qutrit isotropic states. For Werner states, our approach saturates the analytical visibility bounds under three Pauli measurements, arbitrary projective measurements (PVMs), and arbitrary positive operator-valued measurements (POVMs). For isotropic states, we achieve the known analytical bounds under arbitrary PVMs. We further investigate the steerability of this class of states under arbitrary POVMs, and our results suggest that POVMs can offer an advantage over PVMs in revealing the steerability of such 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