A neural network oracle for quantum nonlocality problems in networks

Abstract

Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed probability distribution can be reproduced using only classical resources. This causal inference task is challenging even for simple networks, both analytically and using standard numerical techniques. We propose to use neural networks as numerical tools to overcome these challenges, by learning the classical strategies required to reproduce a distribution. As such, the neural network acts as an oracle, demonstrating that a behavior is classical if it can be learned. We apply our method to several examples in the triangle configuration. After demonstrating that the method is consistent with previously known results, we give solid evidence that the distribution presented in [N. Gisin, Entropy 21(3), 325 (2019)] is indeed nonlocal as conjectured. Finally we examine the genuinely nonlocal distribution presented in [M.-O. Renou et al., PRL 123, 140401 (2019)], and, guided by the findings of the neural network, conjecture nonlocality in a new range of parameters in these distributions. The method allows us to get an estimate on the noise robustness of all examined distributions.

This is a pre-print of an article published in npj Quantum Information. The final authenticated version is available online at: https://doi.org/10.1038/s41534-020-00305-x Implementation can be found at: https://github.com/tkrivachy/neural-network-for-nonlocality-in-networks

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Cited by in corpus (43)

• Bell nonlocality in networks
• Genuine multipartite nonlocality is intrinsic to quantum networks
• Machine Learning meets Quantum Foundations: A Brief Survey
• Entanglement swapping and quantum correlations via Elegant Joint Measurements
• Network Quantum Steering
• A Reinforcement Learning approach for Quantum State Engineering
• Quantifying Quantumness of Channels Without Entanglement
• Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources
• Single-photon nonlocality in quantum networks
• Nonlocality for Generic Networks
• Proofs of network quantum nonlocality in continuous families of distributions
• Building separable approximations for quantum states via neural networks
• Test of Genuine Multipartite Nonlocality
• Towards a minimal example of quantum nonlocality without inputs
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Sharing nonlocality in quantum network by unbounded sequential observers
• Neural-network approach for identifying nonclassicality from click-counting data
• Entanglement Verification with Deep Semi-supervised Machine Learning
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
• Post-quantum nonlocality in the minimal triangle scenario
• Numerically assisted determination of local models in network scenarios
• Neural Network Approach to the Simulation of Entangled States with One Bit of Communication
• Evolving Quantum Circuits
• Detection of Network and Genuine Network Quantum Steering
• Classification of joint quantum measurements based on entanglement cost of localization
• Measuring network quantum steerability utilizing artificial neural networks
• Noise-robust proofs of quantum network nonlocality
• Fast semidefinite programming with feedforward neural networks
• Sharing nonlocality in a network using the quantum violation of chain network inequality
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Multistage games and Bell scenarios with communication
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Unveiling the nonclassicality within quasi-distribution representations through deep learning
• Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing
• Nonlocal correlations in an asymmetric quantum network
• Violation of the Finner inequality in the four-output triangle network
• Local models and Bell inequalities for the minimal triangle network
• Experimental genuine quantum nonlocality in the triangle network
• Topologically noise robust network steering without inputs
• Exploring the Local Landscape in the Triangle Network
• Detection of quantum information masking via machine learning