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arXiv:1506.07380 · Physical Review Letters

Nonlinear Bell Inequalities Tailored for Quantum Networks

Denis Rosset, Cyril Branciard, Tomer Jack Barnea, Gilles Pütz, Nicolas Brunner, Nicolas Gisin

Published Jan 7, 2016• 138 citations
arXivHTMLPDF

Abstract

In a quantum network, distant observers sharing physical resources emitted by independent sources can establish strong correlations, which defy any classical explanation in terms of local variables. We discuss the characterization of nonlocal correlations in such a situation, when compared to those that can be generated in networks distributing independent local variables. We present an iterative procedure for constructing Bell inequalities tailored for networks: starting from a given network, and a corresponding Bell inequality, our technique provides new Bell inequalities for a more complex network, involving one additional source and one additional observer. We illustrate the relevance of our method on a variety of networks, demonstrating significant quantum violations, which could not have been detected using standard Bell inequalities.

DOI
10.1103/physrevlett.116.010403

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In a quantum network, distant observers sharing physical resources emitted by independent sources can establish strong correlations, which defy any classical explanation in terms of local variables. We discuss the characterization of nonlocal correlations in such a situation, when compared to those that can be generated in networks distributing independent local variables. We present an iterative procedure for constructing Bell inequalities tailored for networks: starting from a given network, and a corresponding Bell inequality, our technique provides new Bell inequalities for a more complex network, involving one additional source and one additional observer. We illustrate the relevance of our method on a variety of networks, demonstrating significant quantum violations, which could not have been detected using standard Bell inequalities.
The problem of characterizing classical and quantum correlations in networks is considered. Contrary to the usual Bell scenario, where distant observers share a physical system emitted by one common source, a network features several independent sources, each distributing a physical system to a subset of observers. In the quantum setting, the observers can perform joint measurements on initially independent systems, which may lead to strong correlations across the whole network. In this work, we introduce a technique to systematically map a Bell inequality to a family of Bell-type inequalities bounding classical correlations on networks in a star-configuration. Also, we show that whenever a given Bell inequality can be violated by some entangled state ρ , then all the corresponding network inequalities can be violated by considering many copies of ρ distributed in the star network. The relevance of these ideas is illustrated by applying our method to a specific multi-setting Bell inequality. We derive the corresponding network inequalities, and study their quantum violations.
Abstract We initiate the study of the nonlocal correlations in generic asymmetric quantum networks in a star configuration. Therein, the diverse unrelated sources can emit either partially or maximally entangled states, while the observers employ varying numbers of measurement settings. We propose nonlinear Bell inequalities tailored to the distributed entangled states. Specifically, we demonstrate that the algebraic maximal violations of the proposed nonlinear Bell inequalities are physically achievable within the quantum region. To achieve this, we construct the segmented Bell operators through the cut-graft-mix method applied to the Bell operators in the standard Bell tests. Furthermore, we devise the fitting Bell operators using the sum-of-square approach.
Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers sharing some configuration of many independent physical systems. Here, we show how to construct Bell-type inequalities for correlations arising in any tree-structured network, i.e., networks without cycles. This is achieved by an iteration procedure that in each step allows one to add a branch to the tree-structured network and construct a corresponding Bell-type inequality. We explore our inequalities in several examples, in all of which we demonstrate strong violations from quantum theory.
The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic nonmultilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.
Nonlocal correlation plays an important role in device independent quantum information processing. The standard Bell nonlocality has been well studied with single local hidden variables, however the nonlocal correlations in general networks with several independent quantum sources and distant observers have been far less explored. Here, by using three independent entangled photon sources and recently constructed nonlinear Bell inequalities, we experimentally test the nonlocal correlations in the network scenario with different topologies. The violation of the inequalities can be obtained simply with separate measurements, which is much more favourable from the practical point of view. Our experiment results show a violation as 0.7779±0.0093 for the star network, and 0.7303±0.0024 for the chain network. Furthermore, we demonstrate that more measurement settings for each observer can bound more information against an eavesdropper.
Quantum networks play an important role in the fields of quantum information and quantum computation. One of the current problems for these networks concerns nonlocality. Characterizing and detecting nonlocality is relevant to the implementation of quantum networks and quantum repeaters, where Bell inequalities can be used to test if configurations are prepared correctly. This report contains an overview of an iterative method to find Bell inequalities for networks. Starting from a given network, this method constructs a new Bell inequality for a network containing one additional source and one additional party. We use this procedure to find new Bell inequalities for specific network structures and analyse how these can be used to detect nonlocality within a network. In the first part the Bell inequalities are considered from a more theoretical point of view. We focus on star-shaped networks and discuss violations predicted by quantum mechanics. We look for quantitative bounds describing a set of states that lead to violation, giving an indication of the required quality of the sources. Finally this method is applied to a setup similar to the one described by Bernien et al. We consider a network consisting of three parties and two sources. The effect of errors during preparation of an entangled pair of photons on the ability to detect nonlocality is evaluated. The same is done for the effect of measurement errors. Using numerical computations we show that violation of the Bell inequality can be improved by choosing different measurement angles.