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Journal of Physics A Mathematical and General

Multipartite entangled state of continuum variables generated by an optical network

Hong-Yi Fan, Song Tong-Qiang

Published Jul 2, 2003• 6 citations
Publisher

Abstract

We construct a kind of new multipartite entangled states of continuum variables, which are related to unitary group U ( n ). Using the technique of integral within an ordered product of operators we prove that such states make up a complete representation in multimode Fock space. The new state can be generated by an optical network whose operation on an incoming photon distributes the photon among the outputs according to the unitary group transform. The potential use of the new state in quantum teleportation is briefly discussed.

DOI
10.1088/0305-4470/36/28/309

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We construct a kind of new multipartite entangled states of continuum variables, which are related to unitary group U ( n ). Using the technique of integral within an ordered product of operators we prove that such states make up a complete representation in multimode Fock space. The new state can be generated by an optical network whose operation on an incoming photon distributes the photon among the outputs according to the unitary group transform. The potential use of the new state in quantum teleportation is briefly discussed.
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.
A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.