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arXiv:1808.07069 · Physical Review Letters

Machine Learning Nonlocal Correlations

Askery Canabarro, Samuraí Brito, Rafael Chaves

Published May 22, 2019• 69 citations
arXivHTMLPDF

Abstract

The ability to witness nonlocal correlations lies at the core of foundational aspects of quantum mechanics and its application in the processing of information. Commonly, this is achieved via the violation of Bell inequalities. Unfortunately, however, their systematic derivation quickly becomes unfeasible as the scenario of interest grows in complexity. To cope with that, here, we propose a machine learning approach for the detection and quantification of nonlocality. It consists of an ensemble of multilayer perceptrons blended with genetic algorithms achieving a high performance in a number of relevant Bell scenarios. As we show, not only can the machine learn to quantify nonlocality, but discover new kinds of nonlocal correlations inaccessible with other current methods as well. We also apply our framework to distinguish between classical, quantum, and even postquantum correlations. Our results offer a novel method and a proof-of-principle for the relevance of machine learning for understanding nonlocality.

DOI
10.1103/physrevlett.122.200401

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The ability to witness nonlocal correlations lies at the core of foundational aspects of quantum mechanics and its application in the processing of information. Commonly, this is achieved via the violation of Bell inequalities. Unfortunately, however, their systematic derivation quickly becomes unfeasible as the scenario of interest grows in complexity. To cope with that, here, we propose a machine learning approach for the detection and quantification of nonlocality. It consists of an ensemble of multilayer perceptrons blended with genetic algorithms achieving a high performance in a number of relevant Bell scenarios. As we show, not only can the machine learn to quantify nonlocality, but discover new kinds of nonlocal correlations inaccessible with other current methods as well. We also apply our framework to distinguish between classical, quantum, and even postquantum correlations. Our results offer a novel method and a proof-of-principle for the relevance of machine learning for understanding nonlocality.
As the demand for quantum networks and communication grows, identifying quantum nonlocality in these networks has become a crucial and challenging task. The nonconvex nature of the network local set makes traditional Bell-type inequalities inadequate for detection. Machine learning algorithms have emerged as a promising approach to address this issue. In this study we introduce a quantifier for nonlocality in chain-shaped quantum networks and employ deep-learning algorithms for its detection. We validate this method using the trilocal network, adopting an ensemble learning strategy called the stacking method, which combines four distinct deep neural networks to train a linear regression model. Our results show that machine learning effectively quantifies nonlocality in chain networks and exhibits strong generalization capabilities for Werner states.
Despite the success of quantum mechanics in predicting the outcomes of experiments in many branches of physics, the foundations of the theory have remained subject of research and dispute. At the basis of this struggle with the theory lie the phenomena of nonlocality and entanglement. Since it was first predicted by Bell in 1964, nonlocality was not only verified in numerous experiments, but also identified as a useful resource for quantum information processing. Thus, the study of nonlocality is important both from a fundamental point of view and with respect to new applications in quantum information theory, such as secure cryptography and randomness generation. The identification of entanglement as a resource for quantum information led to a strong theoretical effort devoted to its characterisation and detection. Many of the resulting mathematical tools find application in several domains of physics. Although the only known way to create nonlocal correlations is to measure entangled quantum systems, it has been shown that entanglement and nonlocality constitute two inequivalent properties. Therefore, in the light of the success of entanglement theory, it is of interest to also devise a resource theory of nonlocality. The task of this thesis is to develop such a theoretical framework for the characterisation of nonlocality as a resource. To gain a better understanding of nonlocal correlations it will be necessary to investigate correlation scenarios that go beyond the situation originally considered by Bell. In doing so, this thesis provides new description of nonlocality that also have implications for the characterisation of quantum correlations and the detection of new forms of nonlocality. The first question we address is how nonlocality can consistently be defined in a scenario of arbitrarily many parties that may collaborate among each other. To this end we recognise which are the allowed physical operations in this situation and then define nonlocality as the resource that cannot be created by these operations. Our approach shows that the conventional definition of multipartite nonlocality, adopted by the community so far, is inconsistent with this operational definition; we further propose and analyse new models that do not suffer from these inconsistencies. Furthermore, we show that our findings have implications for the characterisation of quantum correlations. A recent approach to describe the set of quantum correlation consists in using principles inspired from information theory. By using a special instance of the models we defined earlier we show a fundamental limitation of this approach: no bipartite information principle is sufficient to single out the set of quantum correlations from the set of nonsignalling correlations. We then developed a description of nonlocality in an even more generalised scenario of several parties. Motivated by a result of Popescu we study scenarios where the parties are allowed to perform not only a single but sequences of measurements on their systems. Characterising nonlocality also in this scenario in operational terms and defining local models compatible with this definition, we show that a new form of nonlocality can be detected Lastly, we examine the problem of detecting the presence of nonlocality in a multipartite scenario when one is given only partial access to the global system. We find that one can verify that the total system must display nonlocality, even though the accessible subsystems only exhibit local correlations.
Machine learning, the core of artificial intelligence and big data science, is one of today's most rapidly growing interdisciplinary fields. Recently, machine learning tools and techniques have been adopted to tackle intricate quantum many-body problems. In this Letter, we introduce machine learning techniques to the detection of quantum nonlocality in many-body systems, with a focus on the restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning, we demonstrate that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings. Our results build a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.
Machine learning, the core of artificial intelligence and big data science, is one of today's most rapidly growing interdisciplinary fields. Recently, machine learning tools and techniques have been adopted to tackle intricate quantum many-body problems. In this Letter, we introduce machine learning techniques to the detection of quantum nonlocality in many-body systems, with a focus on the restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning, we demonstrate that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings. Our results build a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.
The estimation of the guessing probability has paramount importance in quantum cryptographic processes. It can also be used as a witness for nonlocal correlations. In most of the studied scenarios, estimating the guessing probability amounts to solving a semi-definite programme, for which potent algorithms exist. However, the size of those programs grows exponentially with the system size, becoming infeasible even for small numbers of inputs and outputs. We have implemented deep learning approaches for some relevant Bell scenarios to confront this problem. Our results show the capabilities of machine learning for estimating the guessing probability and for understanding nonlocality.
Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory and at the center of many quantum information processing protocols.Over the years, different perspectives on nonlocality have been put forward as well as different ways to detect nonlocality and quantify it.Unfortunately, and in spite of its relevance, as the complexity of the Bell scenario increases, deciding whether a given observed correlation is nonlocal becomes computationally intractable.Here, we propose to analyze a Bell scenario as a tensor network, a perspective permitting us to test and quantify nonlocality, resorting to very efficient algorithms originating from compressed sensing and that offer a significant speedup in comparison with standard linear programming methods.We use that all nonsignaling correlations can be described by hidden variable models governed by a quasiprobability, a fact we prove with simple linear algebra methods.