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Laser Physics Letters

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

Guo‐Zhu Pan, Shuting Zou, Ming Yang, Jian Zhou, Gang Zhang

Published Dec 27, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ad174e

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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.
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.
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.
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.
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.
Quantum steering, as a cornerstone of quantum information, is usually used to witness the quantum correlation of bipartite and multi-partite states. Here, we experimentally demonstrate the quantum steering inequality of two-qubit mixed states based on the fine-grained uncertainty relation. Our experimental results show that the steering inequality has potent sensitivity to Werner states and Bell diagonal states. The steering strategy exhibits a strong ability to identify that Werner states are steerable when the decoherence coefficient a>12. Compared to the steering inequality obtained by another stratagem, the steering witness criteria of mixed states based on the fine-grained uncertainty relation demonstrated in our experiment has better precision and accuracy. Moreover, the detection efficiency in our measurement setup is only required to be 50% to close the detection loophole, which means our approach needs less detector efficiency to certificate the steerability of mixed states.
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.