80 research outputs found
A neural network oracle for quantum nonlocality problems in networks
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.Comment: 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-network
Uncertainty of Feed Forward Neural Networks Recognizing Quantum Contextuality
The usual figure of merit characterizing the performance of neural networks
applied to problems in the quantum domain is their accuracy, being the
probability of a correct answer on a previously unseen input. Here we append
this parameter with the uncertainty of the prediction, characterizing the
degree of confidence in the answer. A powerful technique for estimating both
the accuracy and the uncertainty is provided by Bayesian neural networks
(BNNs). We first give simple illustrative examples of advantages brought
forward by BNNs, out of which we wish to highlight their ability of reliable
uncertainty estimation even after training with biased data sets. Then we apply
BNNs to the problem of recognition of quantum contextuality which shows that
the uncertainty itself is an independent parameter identifying the chance of
misclassification of contextuality
Fast semidefinite programming with feedforward neural networks
Semidefinite programming is an important optimization task, often used in
time-sensitive applications. Though they are solvable in polynomial time, in
practice they can be too slow to be used in online, i.e. real-time
applications. Here we propose to solve feasibility semidefinite programs using
artificial neural networks. Given the optimization constraints as an input, a
neural network outputs values for the optimization parameters such that the
constraints are satisfied, both for the primal and the dual formulations of the
task. We train the network without having to exactly solve the semidefinite
program even once, thus avoiding the possibly time-consuming task of having to
generate many training samples with conventional solvers. The neural network
method is only inconclusive if both the primal and dual models fail to provide
feasible solutions. Otherwise we always obtain a certificate, which guarantees
false positives to be excluded. We examine the performance of the method on a
hierarchy of quantum information tasks, the Navascu\'es-Pironio-Ac\'in
hierarchy applied to the Bell scenario. We demonstrate that the trained neural
network gives decent accuracy, while showing orders of magnitude increase in
speed compared to a traditional solver
Machine-learning-based device-independent certification of quantum networks
Witnessing nonclassical behavior is a crucial ingredient in quantum information processing. For that, one has to optimize the quantum features a given physical setup can give rise to, which is a hard computational task currently tackled with semidefinite programming, a method limited to linear objective functions and that becomes prohibitive as the complexity of the system grows. Here, we propose an alternative strategy, which exploits a feedforward artificial neural network to optimize the correlations compatible with arbitrary quantum networks. A remarkable step forward with respect to existing methods is that it deals with nonlinear optimization constraints and objective functions, being applicable to scenarios featuring independent sources and nonlinear entanglement witnesses. Furthermore, it offers a significant speedup in comparison with other approaches, thus allowing to explore previously inaccessible regimes. We also extend the use of the neural network to the experimental realm, a situation in which the statistics are unavoidably affected by imperfections, retrieving device-independent uncertainty estimates on Bell-like violations obtained with independent sources of entangled photon states. In this way, this work paves the way for the certification of quantum resources in networks of growing size and complexity
Neural Network Approach to the Simulation of Entangled States with One Bit of Communication
Bell's theorem states that Local Hidden Variables (LHVs) cannot fully explain
the statistics of measurements on some entangled quantum states. It is natural
to ask how much supplementary classical communication would be needed to
simulate them. We study two long-standing open questions in this field with
neural network simulations and other tools. First, we present evidence that all
projective measurements on partially entangled pure two-qubit states require
only one bit of communication. We quantify the statistical distance between the
exact quantum behaviour and the product of the trained network, or of a
semianalytical model inspired by it. Second, while it is known on general
grounds (and obvious) that one bit of communication cannot eventually reproduce
all bipartite quantum correlation, explicit examples have proved evasive. Our
search failed to find one for several bipartite Bell scenarios with up to 5
inputs and 4 outputs, highlighting the power of one bit of communication in
reproducing quantum correlations.Comment: 11 pages, 7 figures, 4 table
Violation of the Finner inequality in the four-output triangle network
Network nonlocality allows one to demonstrate non-classicality in networks
with fixed joint measurements, that is without random measurement settings. The
simplest network in a loop, the triangle, with 4 outputs per party is
especially intriguing. The "elegant distribution" [N. Gisin, Entropy 21, 325
(2019)] still resists analytic proofs, despite its many symmetries. In
particular, this distribution is invariant under any output permutation. The
Finner inequality, which holds for all local and quantum distributions, has
been conjectured to be also valid for all no-signalling distributions with
independent sources (NSI distributions). Here we provide evidence that this
conjecture is false by constructing a 4-output network box that violate the
Finner inequality and prove that it satisfies all NSI inflations up to the
enneagon. As a first step toward the proof of the nonlocality of the elegant
distribution, we prove the nonlocality of the distributions that saturates the
Finner inequality by using geometrical arguments.Comment: 8 pages, 8 figures, Any comments are welcome ([email protected]
Experimental nonclassicality in a causal network without assuming freedom of choice
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modeled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity
Possibilistic approach to network nonlocality
The investigation of Bell nonlocality traditionally relies on joint
probabilities of observing certain measurement outcomes. In this work we
explore a possibilistic approach, where only patterns of possible outcomes
matter, and apply it to Bell nonlocality in networks with independent sources.
We present various algorithms for determining whether a given outcome pattern
can be achieved via classical resources or via non-signaling resources. Next we
illustrate these methods considering the triangle and square networks (with
binary outputs and no inputs), identifying patterns that are incompatible with
the network structure, as well as patterns that imply nonlocality. In
particular, we obtain an example of quantum nonlocality in the square network
with binary outcomes. Moreover, we show how to construct certificates for
detecting the nonlocality of a certain pattern, in the form of nonlinear
Bell-type inequalities involving joint probabilities. Finally, we show that
these inequalities remain valid in the case where the sources in the network
become partially correlated.Comment: 17 pages, lots of figures, comments welcom
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