6533b857fe1ef96bd12b4cb7
RESEARCH PRODUCT
Higher-order Einstein-Podolsky-Rosen correlations and inseparability conditions for continuous variables
E. ShchukinP. Van Loocksubject
PhysicsPure mathematicsGaussianQuantum Physics02 engineering and technologyQuantum entanglementState (functional analysis)Squashed entanglement01 natural sciencesMultipartite entanglement010305 fluids & plasmassymbols.namesakeSeparable stateQuantum mechanics0103 physical sciences0202 electrical engineering electronic engineering information engineeringBipartite graphsymbols020201 artificial intelligence & image processingEPR paradoxdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-03-09 | Physical Review A |