We show that the Agarwal–Simon representation of single-mode squeezed states can be generalized to find new form of three-mode squeezed states. We use the tripartite entangled state representations | p , y , z 〉 and | x , u , v 〉 to realize this goal.
By extending the Einstein-Podolsky-Rosen bipartite entanglement to the tripartite case,we construct the common eigenvector of the tripartite centre-of -mass coordinate and two mass-weighted relative momenta,which is a new entangled state of continuum variables.The classical dilation transform of varibles in such a state induces new entangled state of continum variables,The classical dilation transform of variables in such a state induces a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.