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arXiv:1511.08444 · Physical Review A

Higher-order Einstein-Podolsky-Rosen correlations and inseparability conditions for continuous variables

Evgeny V Shchukin, Peter van Loock

Published Mar 9, 2016• 5 citations
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Abstract

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. We give an explicit example of a non-Gaussian state that exhibits fourth-order but no second-order EPR correlations. Similarly, 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.

DOI
10.1103/physreva.93.032114

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