Abstract. We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-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

Print publication: Issue 5 (8 February 2008)
Received 19 October 2007, in final form 29 November 2007
Published 23 January 2008