title: Multimode uncertainty relations and separability of continuous variable states.
abstract: A multimode uncertainty relation (generalizing the Robertson-Schrödinger 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.
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors.forename: Alessio
authors.initials: A
authors.lastname: Serafini