Higher-order EPR correlations and inseparability conditions for continuous variables

We derive two types of sets of higher-order conditions for bipartite entanglement in terms of continuous variables. One corresponds to an extension of the well-known Duan inequalities from second to higher moments describing a kind of higher-order Einstein-Podolsky-Rosen (EPR) correlations. Only the...

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Bibliographic Details
Published in:arXiv.org 2015-11
Main Authors: Shchukin, E, P van Loock
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Entanglement
Inequalities
Structural hierarchy
Online Access:Get full text
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Summary:We derive two types of sets of higher-order conditions for bipartite entanglement in terms of continuous variables. One corresponds to an extension of the well-known Duan inequalities from second to higher moments describing a kind of higher-order Einstein-Podolsky-Rosen (EPR) correlations. Only the second type, however, expressed by powers of the mode operators leads to tight conditions with a hierarchical structure. We start with a minimization problem for the single-partite case and, using the results obtained, establish relevant inequalities for higher-order moments satisfied by all bipartite separable states. A certain fourth-order condition cannot be violated by any Gaussian state and we present non-Gaussian states whose entanglement is detected by that condition. Violations of all our conditions are provided, so they can all be used as entanglement tests.
ISSN:2331-8422
DOI:10.48550/arxiv.1511.08444