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arXiv:0911.5249

Weyl correspondence method to construct multipartite entangled quantum state

Shuangxi Zhang, Xu Ma, Hong-Yi Fan

Published Nov 27, 2009• 0 citations
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Abstract

Via the Weyl correspondence approach, we construct multipartite entangled state which is the common eigenvector of their center-of-mass coordinate and mass-weighted relative momenta. This approach is concise and effective for setting up the Fock representation of continuous multipartite entangled states. The technique of integration within an ordered product (IWOP) of operators is also essential in our derivation.

DOI
10.48550/arxiv.0911.5249

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Via the Weyl correspondence approach, we construct multipartite entangled state which is the common eigenvector of their center-of-mass coordinate and mass-weighted relative momenta. This approach is concise and effective for setting up the Fock representation of continuous multipartite entangled states. The technique of integration within an ordered product (IWOP) of operators is also essential in our derivation.
Since the commutation relation [x1-x2,a1+a2]=0,their common eigenvector |β,x〉 is constructed by using the technique of integration within an ordered product(IWOP) of operators.This state exhibits the properties of the coherent and entangled states.Its entangled properties and the relations with the EPR entangled state can be confirmed by Schmidt decomposition and the unilateral integral for|β,x〉.The superposition of the states |β=β1+iβ2,x〉 along β1 axis yields the ideal two-mode entangled state.
We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix |ξ 1 , ξ 2 〉 C,D C,D 〈ξ 1 , ξ 2 | is a Radon transform of Wigner operator.