Generalized multi-mode bosonic realization of the SU(1,1) algebra and its corresponding squeezing operator

By constructing a generalized multi-partite entangled state representation and introducing the ket-bra integral in this representation, we find a new set of generalized bosonic realization of the generators of the SU(1, 1) algebra, which can compose a generalized multi-mode squeezing operator. This operator squeezes the multi-partite entangled state in a natural way. Then the corresponding multi-mode squeezed vacuum states |r > is obtained. Based on this, the variances of the n-mode quadratures and the higher-order squeezing in |r > are evaluated. In addition, we examine the violation of the Bell inequality for |r > by using the formalism of Wigner representation.