Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applied Sciences

Improving Steerability Detection via an Aggregate Class Distribution Neural Network

Yuyang Hao, Kan He, Ying Zhang

Published Jul 4, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.3390/app13137874

Related papers

Detecting the steerability bounds of generalized Werner states via a backpropagation neural network

Jun Zhang, Kan He, Ying Zhang +4 more

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.

arXiv:2110.13379•Physical Review A•Mar 3, 2022•16 citations

Detection of quantum steering for the generalized Werner states via artificial neural networks

Guo‐Zhu Pan, Shuting Zou, Ming Yang +2 more

Abstract Quantum steering is an important nonlocal resource and has a wide range of applications in quantum information processing. Although a lot of steering criteria have been proposed, it is still very difficult to efficiently detect quantum steering in experiment. Here we employ machine learning techniques to tackle the problem of quantum steering detection in two-qubit system. The quantum steering and un-steering inequalities are combined together, so as to construct quantum steering classifiers for the generalized Werner states via artificial neural networks. More steerable and unsteerable quantum states can be identified by the classifiers proposed here than by the quantum steering inequality or un-steering inequality, which provides a new way to detect steering with only partial information of the given quantum states. We consider two types of artificial neural networks, one is the single-layer perceptron and the other is the multi-layer perceptron. The result shows that the multi-layer perceptron outperforms the single-layer perceptron in terms of accuracy. Compared with the existing quantum steering criteria, our methods do not require the whole information of the quantum state, and the steering of it is detected by using state-independent measurements, so it is easy to realize in experiment.

Laser Physics Letters•Dec 27, 2023•0 citations

Machine learning for detecting steering in qutrit-pair states

Pu Wang, Zhongyan Li, Hui-Xian Meng

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 ${F}_{1}$, 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, ${F}_{2}$, 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.

arXiv:2502.11365•Physical Review A•Sep 8, 2025•1 citation

Robust Steerability Classification via Key Feature Extraction and Matrix Structure Preservation

Yutao Xin, Huixian Meng, Zhongyan Li +1 more

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

quant-pharXiv:2606.04363•Jun 4, 2026•0 citations

Steerability detection of quantum states in qubit-qutrit systems via machine learning

Yu Zhang, Pu Wang, MENG HuiXian +1 more

Inspired by the research on detecting the steerability of two-qubit states via machine learning, this study explores the detection of steerability in qubit-qutrit systems using various machine learning methods. It is found that, (1) for random states, Werner states, and UN states (a newly constructed class of entangled states where Alice cannot steer Bob), there always exist supervised or semi-supervised machine learning methods with a steering detectability accuracy rate of over 95%; (2) the steering bounds predicted by the supervised machine learning methods are mostly higher than the non-steerable bounds provided by theory and lower than the steering bounds determined by the semidefinite programming (SDP). This demonstrates that the machine learning methods are reliable for detecting the steerability of quantum states in qubit-qutrit systems and can detect more steering states compared with the SDP method. It lays the foundation for utilizing machine learning methods to detect quantum states' steerability in bipartite and high-dimensional systems.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Oct 23, 2024•1 citation

Robust steerability classification via key feature extraction

Yutao Xin, Hui-Xian Meng, Zhongyan Li +1 more

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.

Physica Scripta•Sep 11, 2026•0 citations
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.
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 nonlocal resource and has a wide range of applications in quantum information processing. Although a lot of steering criteria have been proposed, it is still very difficult to efficiently detect quantum steering in experiment. Here we employ machine learning techniques to tackle the problem of quantum steering detection in two-qubit system. The quantum steering and un-steering inequalities are combined together, so as to construct quantum steering classifiers for the generalized Werner states via artificial neural networks. More steerable and unsteerable quantum states can be identified by the classifiers proposed here than by the quantum steering inequality or un-steering inequality, which provides a new way to detect steering with only partial information of the given quantum states. We consider two types of artificial neural networks, one is the single-layer perceptron and the other is the multi-layer perceptron. The result shows that the multi-layer perceptron outperforms the single-layer perceptron in terms of accuracy. Compared with the existing quantum steering criteria, our methods do not require the whole information of the quantum state, and the steering of it is detected by using state-independent measurements, so it is easy to realize in experiment.
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{F}_{1}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{F}_{2}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.
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
Inspired by the research on detecting the steerability of two-qubit states via machine learning, this study explores the detection of steerability in qubit-qutrit systems using various machine learning methods. It is found that, (1) for random states, Werner states, and UN states (a newly constructed class of entangled states where Alice cannot steer Bob), there always exist supervised or semi-supervised machine learning methods with a steering detectability accuracy rate of over 95%; (2) the steering bounds predicted by the supervised machine learning methods are mostly higher than the non-steerable bounds provided by theory and lower than the steering bounds determined by the semidefinite programming (SDP). This demonstrates that the machine learning methods are reliable for detecting the steerability of quantum states in qubit-qutrit systems and can detect more steering states compared with the SDP method. It lays the foundation for utilizing machine learning methods to detect quantum states' steerability in bipartite and high-dimensional systems.
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.