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Europhysics Letters (EPL)

Common eigenstates of many-particle compatible observables

Nian-Quan Jiang, Bai-Qi Jin, Yi Zhang, Gen-Chang Cai

Published Sep 22, 2008• 32 citations
Publisher

Abstract

We introduce common eigenstates of many-particle compatible observables in n -mode Fock space. These states make a complete and orthogonal set and can be realized by the use of beam splitter devices. The entanglement properties of these states are exhibited, their applications in solving many-body problems and in quantum communication are shown.

DOI
10.1209/0295-5075/84/14002

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We introduce common eigenstates of many-particle compatible observables in n -mode Fock space. These states make a complete and orthogonal set and can be realized by the use of beam splitter devices. The entanglement properties of these states are exhibited, their applications in solving many-body problems and in quantum communication are shown.
We give common eigenkets of three compatible observables {P1+P2+P3,{P}_{1}{+P}_{2}{+P}_{3},P1​+P2​+P3​, $({\ensuremath{\mu}}_{2}{Q}_{2}+{\ensuremath{\mu}}_{3}{Q}_{3})/({\ensuremath{\mu}}_{2}+{\ensuremath{\mu}}_{3})\ensuremath{-}{Q}_{1},$ ${Q}_{3}\ensuremath{-}{Q}_{2}$}, which are composed of three particles' coordinate Qi{Q}_{i}Qi​ and momentum Pi,{P}_{i},Pi​, where ${\ensuremath{\mu}}_{i}{=m}_{i}{/(m}_{1}{+m}_{2}{+m}_{3}).$ This set of operators are so-called Jacobi coordinates and momenta. By compatible we mean such observables can be simultaneously determined. Using the technique of integration within an ordered product of operators, we prove that the common eigenkets are complete and orthonormal, and hereby qualified for making up a representation. Applying this representation to solving some new three-body problems is also shown.
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.