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arXiv:1811.06658 · Physical Review Letters

Experimental Simultaneous Learning of Multiple Nonclassical Correlations

Mu Yang, Changliang Ren, Yuechi Ma, Ya Xiao, Xiang-Jun Ye, Lulu Song, Jin‐Shi Xu, Man‐Hong Yung, Chuan‐Feng Li, Guang‐Can Guo

Published Nov 6, 2019• 46 citations
arXivHTMLPDF

Abstract

Nonclassical correlations can be regarded as resources for quantum information processing. However, the classification problem of nonclassical correlations for quantum states remains a challenge, even for finite-size systems. Although there exists a set of criteria for determining individual nonclassical correlations, a unified framework that is capable of simultaneously classifying multiple correlations is still missing. In this Letter, we experimentally explored the possibility of applying machine-learning methods for simultaneously identifying nonclassical correlations. Specifically, by using partial information, we applied an artificial neural network, support vector machine, and decision tree for learning entanglement, quantum steering, and nonlocality. Overall, we found that, for a family of quantum states, all three approaches can achieve high accuracy for the classification problem. Moreover, the run time of the machine-learning methods to output the state label is experimentally found to be significantly less than that of state tomography.

DOI
10.1103/physrevlett.123.190401

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Nonclassical correlations can be regarded as resources for quantum information processing. However, the classification problem of nonclassical correlations for quantum states remains a challenge, even for finite-size systems. Although there exists a set of criteria for determining individual nonclassical correlations, a unified framework that is capable of simultaneously classifying multiple correlations is still missing. In this Letter, we experimentally explored the possibility of applying machine-learning methods for simultaneously identifying nonclassical correlations. Specifically, by using partial information, we applied an artificial neural network, support vector machine, and decision tree for learning entanglement, quantum steering, and nonlocality. Overall, we found that, for a family of quantum states, all three approaches can achieve high accuracy for the classification problem. Moreover, the run time of the machine-learning methods to output the state label is experimentally found to be significantly less than that of state tomography.
Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in "big data." A crossover between quantum information and machine learning represents a new interdisciplinary area stimulating progress in both fields. Traditionally, a quantum state is characterized by quantum-state tomography, which is a resource-consuming process when scaled up. Here we experimentally demonstrate a machine-learning approach to construct a quantum-state classifier for identifying the separability of quantum states. We show that it is possible to experimentally train an artificial neural network to efficiently learn and classify quantum states, without the need of obtaining the full information of the states. We also show how adding a hidden layer of neurons to the neural network can significantly boost the performance of the state classifier. These results shed new light on how classification of quantum states can be achieved with limited resources, and represent a step towards machine-learning-based applications in quantum information processing.
The paper suggest employing machine learning for resource-efficient classification of quantum correlations in entanglement distribution networks. Specifically, artificial neural networks (ANN) are utilized to classify quantum correlations based on collective measurements conducted in the geometry of entanglement swapping. ANNs are trained to categorize two-qubit quantum states into five mutually exclusive classes depending on the strength of quantum correlations exhibited by the states. The precision and recall of the ANN models are analyzed as functions of the quantum resources consumed, i.e. the number of collective measurements performed.
Higher-dimensional quantum systems are attracting interest for improving quantum protocol performance by increasing memory space. Characterizing quantum resources of such systems is fundamental but experimentally costly. We tackle the first non-trivial example: a qubit-ququart system, focusing on partial-transpose spectral classification. Entanglement distillation extracts maximally entangled states from noisy resources, but determining distillability typically requires full state tomography, experimentally prohibitive for high-dimensional systems. We explore a machine learning framework to classify distillable bipartite quantum states using fewer measurements than complete tomography. Our approach employs the PPT criterion, categorizing states by negative eigenvalues in the partial transpose. We use various ML algorithms, including Support Vector Machines, Random Forest, and Artificial Neural Networks, with features from fixed measurements and learnable observables. Results show learnable observables consistently outperform Collective Measurement Witnesses methods. While all models distinguish between non-distillable (PPT) and distillable (NPT) states, differentiating NPT subclasses remains challenging, underscoring the intricate Hilbert space geometry. This work provides an experimentally friendly tool for distillability verification in high-dimensional quantum systems without full state reconstruction
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.
Abstract In quantum information science, a major challenge is to look for an efficient means for classifying quantum states. An attractive proposal is to utilize Bell’s inequality as an entanglement witness, for classifying entangled state. The problem is that entanglement is necessary but not sufficient for violating Bell’s inequalities, making these inequalities unreliable in state classification. Furthermore, in general, classifying the separability of states, even for only few qubits, is resource-consuming. Here we look for alternative solutions with the methods of machine learning, by constructing neural networks that are capable of simultaneously encoding convex sets of multiple entanglement witness inequalities. The simulation results indicated that these transformed Bell-type classifiers can perform significantly better than the original Bell’s inequalities in classifying entangled states. We further extended our analysis to classify quantum states into multiple species through machine learning. These results not only provide an interpretation of neural network as quantum state classifier, but also confirm that neural networks can be a valuable tool for quantum information processing.
Quantum state classification and entanglement quantification are of significant importance in the fundamental research of quantum information science and various quantum applications. Traditional methods, such as quantum state tomography, face exponential measurement demands with increasing numbers of qubits, necessitating more efficient approaches. Recent work has shown promise in using artificial neural networks (ANNs) for quantum state analysis. However, existing ANNs may falter when confronted with states affected by dephasing noise, especially with limited data and computational resources. In this study, we employ a machine-learning approach to investigate the disentanglement process in two-qubit systems in the presence of dephasing noise. Our findings highlight the limitations of general state-trained ANNs in classifying states under dephasing noise. Specialized ANN algorithms, tailored for classifying states and quantifying entanglement in such noisy environments, demonstrate excellent performance using only a subset of tomographic features.