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Journal of Physics A Mathematical and Theoretical

Multipartite entangled state representation and squeezing of then-pair entangled state

Junhua Chen, Hong-Yi Fan, Gang Ren

Published May 26, 2010• 3 citations
Publisher

Abstract

We show that the best way to study the relationship between quantum entanglement and quantum squeezing for the multimode case is through constructing the new n -pair entangled state representation . The explicit form of the 2 n -mode squeezing operator which squeezes the n -pair entangled state can be directly derived via the transition from to where M is an n × n complex matrix, and the technique of integration within an ordered product of operators. We also analyze the squeezing properties of the 2 n -mode squeezed state for M being Hermitian, and obtain the variances of the 2 n -mode quadrature operators in the 2 n -mode squeezed vacuum state with a concise result; the condition for reaching the minimum of the uncertainty relationship is also investigated.

DOI
10.1088/1751-8113/43/25/255302

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We show that the best way to study the relationship between quantum entanglement and quantum squeezing for the multimode case is through constructing the new n -pair entangled state representation . The explicit form of the 2 n -mode squeezing operator which squeezes the n -pair entangled state can be directly derived via the transition from to where M is an n × n complex matrix, and the technique of integration within an ordered product of operators. We also analyze the squeezing properties of the 2 n -mode squeezed state for M being Hermitian, and obtain the variances of the 2 n -mode quadrature operators in the 2 n -mode squeezed vacuum state with a concise result; the condition for reaching the minimum of the uncertainty relationship is also investigated.
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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.