Multimode uncertainty relations and separability of continuous variable states

Abstract

A multimode uncertainty relation (generalising the Robertson-Schroedinger relation) is derived as a necessary constraint on the second moments of n pairs of canonical operators. In turn, necessary conditions for the separability of multimode continuous variable states under (m+n)-mode bipartitions are derived from the uncertainty relation. These conditions are proven to be necessary and sufficient for (1+n)-mode Gaussian states and for (m+n)-mode bisymmetric Gaussian states.

4 pages, no figures; shorter version of a longer version (see quant-ph/0508231), published

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Cited by in corpus (7)

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• Correlation Matrices of Two-Mode Bosonic Systems
• Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators
• Canonical and micro-canonical typical entanglement of continuous variable systems
• Entanglement conditions for multi-mode states
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Optical implementation and entanglement distribution in Gaussian valence bond states