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arXiv:2004.08231 · Physical Review A

Characterizing quantum correlations in a fixed-input n -local network scenario

Kaushiki Mukherjee, Biswajit Paul, Arup Roy

Published Mar 19, 2020• 23 citations
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Abstract

Contrary to the Bell scenario, quantum nonlocality can be exploited even when all the parties do not have freedom to select inputs randomly. Such manifestation of nonlocality is possible in networks involving independent sources. One can utilize such a feature of quantum networks for purpose of entanglement detection of bipartite quantum states. In this context, we characterize correlations simulated in networks involving a finite number of sources generating quantum states when some parties perform fixed measurement. Beyond bipartite entanglement, we inquire the same for networks involving sources now generating pure tripartite quantum states. Interestingly, here also randomness in input selection is not necessary for every party to generate nonlocal correlation.

DOI
10.1103/physreva.101.032328

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Contrary to the Bell scenario, quantum nonlocality can be exploited even when all the parties do not have freedom to select inputs randomly. Such manifestation of nonlocality is possible in networks involving independent sources. One can utilize such a feature of quantum networks for purpose of entanglement detection of bipartite quantum states. In this context, we characterize correlations simulated in networks involving a finite number of sources generating quantum states when some parties perform fixed measurement. Beyond bipartite entanglement, we inquire the same for networks involving sources now generating pure tripartite quantum states. Interestingly, here also randomness in input selection is not necessary for every party to generate nonlocal correlation.
Branciard et al. [Phys. Rev. Lett. 104, 170401 (2010)] first characterized the correlations arising in an entanglement swapping network under the assumption that the sources generating the initially uncorrelated quantum systems are independent. Precisely speaking, Branciard et al. [Phys. Rev. Lett. 104, 170401 (2010) and later in Phys. Rev. A 85, 032119 (2012)] analyzed the importance of bilocal (source independence) assumption to lower the restrictions over correlations for revealing quantumness in the network where each of two sources generates a bipartite entangled state. In this context, one may find interest to characterize correlations in a network involving independent sources which can correlate more than two initially uncorrelated multipartite entangled quantum systems. Our present topic of discussion basically analyzes such a network scenario. Specifically, we introduce a trilocal network scenario where each of three sources independently generates a tripartite entangled quantum system, thereby exploring the role of source independence assumption to exploit nonlocality in a network involving multipartite entanglement analogous to bilocal assumption in a network where only bipartite entanglement was considered. Interestingly, genuine entanglement content did not turn out to be an essential requirement for exploiting nonlocality in such a scenario. Moreover, it is interesting to explore whether such a scenario can be generalized so as to characterize correlations arising in a network involving nnn number of nnn-partite systems for any finite value of $n\ensuremath{\ge}4$ under source independence assumption.
Correlations in quantum networks with independent sources exhibit a completely novel form of nonclassicality in the sense that the nonlocality of such correlations can be demonstrated in fixed local input scenarios. Before the pioneering work of Renou et al. [Phys. Rev. Lett. 123, 140401 (2019)], the nonlocal feature of such network correlations was directly attributable to standard Bell nonlocality. In the above-mentioned reference, the authors provided some of the first examples of triangle network correlations, whose nonlocality cannot be deduced from Bell-CHSH nonlocality. To date, a complete characterization of such scenarios has yet to be provided. The present work characterizes correlations arising due to fixed local measurements in a triangle network under a source independence assumption. Precisely speaking, a set of criteria is framed in the form of Bell-type inequalities, each of which is necessarily satisfied by trilocal correlations. Possible quantum violation of at least one criterion from the set is analyzed, which in turn points out the utility of the set of criteria to detect nonlocality (nontrilocality) in quantum triangle networks. Interestingly, measurement on a local product state basis turns out to be sufficient to generate nontrilocal correlations in some quantum networks. Noise tolerance of the detection criteria is discussed followed by a generalization of the framework for demonstrating correlations in any nnn-sided polygon where nnn is finite.
Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to the standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non-nnn-locality in two distinct network topologies (linear and star). We have studied the extremal violations of nnn-local inequalities (compatible with linear and star network) for any fixed amount of entanglement (in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non-nnn-locality in a linear network. However, the same is not true for star nnn-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-nnn-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the nnn-local inequalities is also provided. Interestingly, detection of non-nnn-locality is ensured in the network if product of concurrence of all the sources involved exceeds 12.\frac{1}{2}.21​.
In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum networks.
Quantum nonlocality arising from entangled particles cannot be explained by any classical notion of local causality. In the standard Bell scenario with a source and two measurement stations, entangled states can lose their ability to exhibit nonlocality due to noisy conditions. Given the fundamental and technological significance of nonlocality and the fact that these noisy entangled states can naturally arise in practical situations, it is of utmost importance to unveil their nonlocality. Here, we demonstrate that nonlocal correlations can be generated from quantum states that cannot show nonlocality in bipartite Bell scenarios. We show how to robustly characterize these states and experimentally activate their nonlocality when embedded in a photonic network, by violating classical constraints in this quantum network. These results have implications in foundations of quantum nonlocality and direct applications to quantum technologies by significantly increasing the robustness of nonlocal correlations to noise.
The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.