Multi-partite squeezed states and SU(1,1) symmetry

Quantum optical networks (QONs) are among the best candidates for implementation in quantum information processing (QIP) and quantum communication (QC) over long distances. More specifically, linear QONs (LQONs) comprise passive and active optical devices such as beam splitters and squeezers, respectively, which have been used in a variety of quantum tasks such as quantum state/secret sharing, and quantum teleportation. LQONs are Gaussian preserving and can be characterized by the symplectic group, Sp (2n,R).

Squeezing is a source of entanglement and thus one of the key tools in QIP and QC. Recently, tripartite squeezed states have been produced experimentally via such LQONs, and have been characterized theoretically based on the type of input states. We have developed an elegant and simple mathematical framework, which is a three-mode realization of SU(1,1), for characterizing such schemes. Consequently, regardless of the type of input states, the tripartite squeezed states that are generated can be characterized as SU(1,1) coherent states. Inspired by the elegance of this approach, we have generalized it to a multi-mode realization of SU(1,1) that characterizes a large class of multi-mode squeezed states that are generated in LQONs comprise a two-mode squeezer and passive optical devices, or by concatenating such LQONS to each other. This approach gives us a new insight into the properties of multi-mode squeezed states generated in complex LQONs.