**A new approach to mutlipartite squeezed states**

An efficient technique to characterize complex linear quantum optical networks comprised by passive and active optical devices is the use of the symplectic Lie group, Sp(2n, R). Such optical networks play a significant role in the context of quantum information processing, and have been used in a variety of quantum schemes such as quantum teleportation [1] and quantum state/secret sharing [2]. In general, the operation of a multiport network of this type on a Gaussian input state can be described by Sp(2n, R) transformations, which preserve Gaussian states. The key tool in such quantum optical experiments is the generation and application of squeezed states. Recently, three-mode squeezed states have been produced in several quantum schemes. For characterizing such schemes, we have established a three-mode realization of SU(1, 1), which is a subgroup of Sp(6, R), and consequently the three-mode squeezed states are the coherent states of SU(1, 1). The elegance of this approach helps us to generalize it to multi-mode realizations of SU(1, 1), and to use them for characterizing any multiport quantum optical network constructed by concatenating sections, each with one two-mode squeezer and several passive optical devices. Such realizations give us a new insight into the interesting properties of the multimode squeezed states generated by any complex quantum optical network of this type. References: [1] N. Takei et al., Phys. Rev. A, 72, 042304 (2005). [2] A.M. Lance et al, Phys. Rev. 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