Complementarity of genuine multipartite Bell nonlocality

Abstract

We introduce a new feature of no-signaling (Bell) non-local theories, namely, when a system of multiple parties manifests genuine non-local correlation, then there cannot be arbitrarily high nonlocal correlation among any subset of the parties. We call this feature, complementarity of genuine multipartite non-locality. We use Svetlichny's criterion for genuine multipartite non-locality and nonlocal games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of monogamy of non-locality. As a consequence, we obtain tighter non-trivial monogamy relations that take into account genuine multipartite non-locality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of non-locality. arXiv:1603.09120v4 [quant-ph]

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

“…DISCUSSION AND CONCLUSION EPR steering analyzed in this paper are arbitrary bipartite separations of a tripartite and four-mode Gaussian weighted graph states based on the necessary and sufficient criterion under Gaussian measurements [40], which quantifies EPR steering for bipartite separations of a multipartite Gaussian state. A quantum system involving more than three subsystems has different possible partitions, and it has been discussed for entanglement [43][44][45] and Bell nonlocality [46,47]. For EPR steering of Gaussian states, the criterion which is used to quantify the quantum steering for multipartition of a multipartite Gaussian state remains an open question until now and it is worthy of further investigation.…”

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“…Nonlocality is one of the most fundamental properties of quantum theory. In recent years, nonlocal correlations were found to be useful in many applications in quantum information theory; see, e.g., [3,5,6,[9][10][11]13,21,24]. Initially, nonlocality was considered in a bipartite case.…”

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