New representation of n-mode squeezed state gained via n-partite entangled state

Gang Ren, Hong-Yi Fan

Nian-Quan Jiang, Fan Hong‐Yi

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.

Hong-Yi Fan, Nian-Quan Jiang, Lu Hai-Liang

Hong‐Chun Yuan, Heng-Mei Li, Hong-Yi Fan

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.

姜年权

By extending the Einstein-Podolsky-Rosen (EPR) bipartite entanglement to an n-partite case, we construct the common eigenstate of the n-partite total coordinate and relative momenta for the continuous variables. The entanglement property of the state is shown. The classical dilation transform of variables in such a state induces a new n-mode squeezing operator related to an n-mode bosonic operator realization of SU(1,1) Lie algebra.

G. S. Agarwal, R. Simon