SU(1,1) symmetry of multimode squeezed states

Abstract

We show that a class of multimode optical transformations that employ linear optics plus twomode squeezing can be expressed as SU(1,1) operators. These operations are relevant to stateof-the-art continuous variable quantum information experiments including quantum state sharing, quantum teleportation, and multipartite entangled states. Using this SU(1,1) description of these transformations, we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often-used restriction to Gaussian states. We analyze this basis, show its application to a class of transformations, and discuss its extension to more general quantum optical networks. PACS numbers: 03.65.Fd, 42.50.Ex, 03.67.-a I.