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, a neural network acts as an oracle for an observed behavior, demonstrating that it 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 a quantum distribution recently proposed by Gisin is indeed nonlocal as conjectured. Finally we examine the genuinely nonlocal distribution recently presented by Renou et al., 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.

Multistage games and Bell scenarios with communication

“…A particularly interesting venue would be to consider the relation between Bell scenario relaxing the measurement independence ("free-will") assumption and the kind of games discussed by Forges [63] where the advice might be correlated with the types of the players. Finally, machine learning has been recently shown to provide an alternative manner to characterize Bell correlations as well as optimize Bell inequalities [64][65][66][67][68]. Given the connection between Bell scenarios and game theory, another relevant path for future research is to understand whether machine learning might also be applied to the analysis of equilibrium points and optimal payoffs.…”

Building separable approximations for quantum states via neural networks

“…The central idea of this work is to use a neural network as a variational ansatz for the density matrix by representing the local components of the separable decomposition with a single neural network. The approach is inspired by a similar approach taken for nonlocality, where neural networks represent the local components of a Bell-local behavior [54].…”

Quantifying Quantumness of Channels Without Entanglement

“…The extension of quantum physics into the realm of information theory is important both for fundamental physics and for practical applications, such as quantum computing, quantum cryptography [1], and quantum random number generation [2,3]. For the latter examples, the practical implementation of entangled based, device-independent, and one-side device-independent quantum information tasks [4][5][6][7][8] relies on the quantum resources, e.g., entangled [9][10][11], steerable [12][13][14][15], and nonlocal states [16][17][18][19][20], respectively. Extending these ideas to quantum networks [21][22][23][24], one needs reliable quantum devices (e.g., quantum communication lines [25] and quantum repeaters [26,27]) to transmit or generate quantum resources between nodes (senders and receivers) in the network.…”