Analyzing shareability of correlations arising in any physical theory may be considered as a fruitful technique of studying the theory. Our present topic of discussion involves an analogous approach of studying quantum theory. For our purpose, we have deviated from the usual procedure of assessing monogamous nature of quantum correlations in standard Bell-CHSH scenario. We have considered correlations arising in a quantum network involving independent sources. Precisely speaking, we have analyzed monogamy of nonbilocal correlations by deriving a relation restricting marginals. Interestingly, restrictions constraining distribution of nonbilocal correlations remain same irrespective of whether inputs of the nodal observers are kept fixed(in different bilocal networks) while studying nonbilocal nature of marginal correlations.
Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n -locality scenario consisting of n two-qubit quantum states distributed among n + 1 nodes of a star-shaped network.
The nonlocality revealed in a multiparty multisource network Bell experiment is conceptually different than the standard multiparty Bell nonlocality involving a single common source. Here, by introducing variants of asymmetric bilocal as well as trilocal network scenarios, we go beyond the typical bilocal network scenario where both the edge parties have an equal number of measurement settings. We first introduce an asymmetric bilocal network where one of the edge parties (say, Alice) receives ${2}^{n\ensuremath{-}1}$ inputs and the other edge party (say, Charlie) receives
n inputs. We derive two variants of asymmetric bilocality inequalities and demonstrate their optimal quantum violations. Further, we explore two types of asymmetric trilocal scenarios: (i) when two edge parties receive ${2}^{n\ensuremath{-}1}$ inputs each and the other edge party receives
n inputs, and (ii) when one edge party receives ${2}^{n\ensuremath{-}1}$ inputs and the other two edge parties have
n inputs each. We use an elegant sum-of-squares technique that enables us to evaluate the quantum optimal values of the proposed network inequalities without assuming the dimension of the systems for both the asymmetric bilocal as well as the trilocal scenarios. Further, we demonstrate the robustness of the quantum violations of the proposed inequalities in the presence of white noise.