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IEEE International Conference on Software Quality, Reliability and Security Companion (QRS-C)

Characterization of Nonlocality in Chained Quantum Networks

Ya-Qi Dong, Yuqian Zhou, Qian-Kun Yao

Published Dec 1, 2022• 1 citation
Publisher

Abstract

Quantum information processing shows its superiority and particularity over classical information processing. One of the main characteristics that distinguishes quantum network from classical network is its nonlocality. The characterization and quantification of quantum nonlocality is the core task of quantum information and has great significance. In this paper, we study the nonlocality of a chain quantum network with three sources and four participants, construct a 3-local Bell inequality, and prove its quantum violation. Our results will promote the construction efficiency of Bell inequalities and contribute theoretical significance for quantum non-locality.

DOI
10.1109/qrs-c57518.2022.00082

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Quantum information processing shows its superiority and particularity over classical information processing. One of the main characteristics that distinguishes quantum network from classical network is its nonlocality. The characterization and quantification of quantum nonlocality is the core task of quantum information and has great significance. In this paper, we study the nonlocality of a chain quantum network with three sources and four participants, construct a 3-local Bell inequality, and prove its quantum violation. Our results will promote the construction efficiency of Bell inequalities and contribute theoretical significance for quantum non-locality.
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.
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.
Abstract Recently, a class of innovative notions on quantum network nonlocality (QNN), called full quantum network nonlocality (FQNN), have been proposed in Phys. Rev. Lett. 128 010403 (2022). As the generalization of full network nonlocality (FNN), l-level quantum network nonlocality (l-QNN) was defined in arxiv. 2306.15717 quant-ph (2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.
Quantum nonlocality in networks featuring multiple independent sources underpins large-scale quantum communication and poses fundamental challenges for its characterization. In this work, we construct a family of explicit nonlinear Bell inequalities to verify the nonlocality across the general multi-input quantum networks. The construction of these inequalities relies on the number of leaf nodes, a network parameter that can be identified by a linear-time algorithm. Our approach establishes a structural connection between bipartite full-correlation Bell inequalities and network Bell inequalities, enabling the analytical derivation of optimal quantum violations and the conditions under which they occur. We further quantify the upper bound on maximal violations achievable by arbitrary two-qubit mixed states in such networks, under separable measurements, and evaluate the noise robustness of the proposed inequalities via the visibilities of noisy states. Finally, we demonstrate that these inequalities can, in a device-independent manner, distinguish between network topologies of equal size that differ in the number of leaf nodes.
Network Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in sevaral quantum information processing tasks. Here, we are focusing on how the role of the independence of the measurement choices of the end parties in a network works and can be used to enhance the security in a quantum network. In both three-parties two-sources bilocal network and four-parties three-sources star network scenarios, we are able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communications. Theoratically, we have proved that by relaxing the independence of the measurement choices of only one end party we can create a Standard Network Nonlocality(SNN) and more stronger Full Network Nonlocality(FNN) and we can get maximum quantum violation by the classical no-signalling local model. We are able to distinguish between two types of network nonlocality in the sense that the FNN is stronger than SNN, i.e., FNN states all the sources in a network need to distribute nonlocal resources.