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Journal of Physics A Mathematical and General

Einstein-Podolsky-Rosen entanglement for self-interacting complex scalar fields

Hong-Yi Fan, Zeng‐Bing Chen

Published Feb 26, 2001• 1 citation
Publisher

Abstract

We demonstrate the Einstein-Podolsky-Rosen (EPR) correlations in the Gaussian trial wavefunctional widely used in the Schrödinger representation of the self-interacting complex scalar fields (CSF). This demonstration is based on the explicit eigenstates ||ξ⟩, which possess the precise EPR entanglement and constitute a complete and orthonormal representation, of CSF ϕ and ϕ † in the Fock space. To show the entanglement of the Gaussian trial wavefunctional, we evaluate in the ⟨ξ||-representation its `entangled' Wigner functional resembling the Wigner function of the two-mode squeezed vacuum state, whose quantum entanglement is well known.

DOI
10.1088/0305-4470/34/9/304

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We demonstrate the Einstein-Podolsky-Rosen (EPR) correlations in the Gaussian trial wavefunctional widely used in the Schrödinger representation of the self-interacting complex scalar fields (CSF). This demonstration is based on the explicit eigenstates ||ξ⟩, which possess the precise EPR entanglement and constitute a complete and orthonormal representation, of CSF ϕ and ϕ † in the Fock space. To show the entanglement of the Gaussian trial wavefunctional, we evaluate in the ⟨ξ||-representation its `entangled' Wigner functional resembling the Wigner function of the two-mode squeezed vacuum state, whose quantum entanglement is well known.
Our primary purpose of this work is to explicitly construct the general multipartite Einstein–Podolsky–Rosen (EPR) entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.
For complex scalar fields ( x ) and ( x ), we introduce the entangled states which are their common eigenvectors. The states possessing complete and orthonormal properties are a field-theoretical generalization of the Einstein-Podolsky-Rosen pair states in quantum mechanics. Based on the new representation, we obtain the complete and orthonormal states { q }, r , the common eigenvectors of the charge operator and ( x ) ( x ) , with which the charge lowering and raising operators can be naturally defined. The applications of our formulation are briefly discussed.
The Einstein–Podolsky–Rosen (EPR) wavefunction is a two-particle wavefunction that is a simultaneous eigenfunction of the relative coordinate and the centre-of-mass momentum. The Fock space representation of this function is easily obtained as a direct product of an eigenfunction of the relative coordinate and an eigenfunction of the centre-of-mass momentum. Straightforward generalization to an arbitrary number of particles is shown to be feasible, and a classification of multiparticle entangled states is outlined. The relation between entanglement and inseparability is pointed out, and the status of the EPR states within the much broader family of entangled states is emphasized.