Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

Abstract

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 a growing attention, but a deep characterization of quantum behaviour 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 separable 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 projective separable 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 n-locality scenario consisting of n two-qubit quantum states distributed among n + 1 nodes of a star-shaped network.

Preservation of quantum nonbilocal correlations in noisy entanglement-swapping experiments using weak measurements

“…. The maximum of the quantity B 22 can be calculated following the method described in [26]. Using Eq.…”

Nonlocality of all quantum networks

“…Recently, nonlinear Bell-type inequalities are proposed for verifying the non-trilocality [40] or non-bilocality [6,41] of correlations originating from the standard entanglement swapping. It is then extended for star-shaped networks [43] or small-sized networks [44,45]. Another procedure is iteratively expanding a given network into the desired network [46].…”

“…It follows a new joint conditional probability distribution asSimilar to verifying single entanglement [2, 8], how to decide the nonlocality of a quantum network is also a fundamental question. Nevertheless, identifying the nonlocality of a general quantum network remains an extremely difficult problem [40][41][42][43][44][45][46][47].Here, we introduce a new framework for exploring the nonlocality of all quantum networks. Given a quantum network consisting of a joint quantum system ρ = ρ 1 ⊗ · · · ⊗ ρ k shared by n observers, the main idea is to create quantum subnetworks for special observers (Alice and Charlie shown in Figure 1).…”

“…Additionally, the proof of Theorem 1 also provided an interesting by-product that universal Bell inequality exists for detecting a single entanglement by using local projection and entanglement distilling [1].Nonlocality of all connected quantum networks. The Λ-shaped quantum network can be generalized to chain-shaped quantum networks [7,46] or star-shaped quantum networks with several observers [7,43,46]. Here, we further consider a general quantum network N q with the connectivity in its schematic graph scenario.…”

“…Similar to verifying single entanglement [2, 8], how to decide the nonlocality of a quantum network is also a fundamental question. Nevertheless, identifying the nonlocality of a general quantum network remains an extremely difficult problem [40][41][42][43][44][45][46][47].…”