理论物理通讯：英文版

Entanglement of the Common Eigenvector of Two Particles‘ Center—of—Mass Coordinate and Mass—Weighted Relative Momentum

FANHong-Yi, SUNMing-Zhai

Published Jan 1, 2002• 0 citations

Abstract

We reveal that the common eigenvector of two particles' center-of-mass coordinate and mass-weightedrelative momentum is an entangled state. Its Schmidt decomposition exhibits that the entanglement involves squeezingwhich depends on the ratio of two particles' masses. The corresponding entangling operators are derived.

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理论物理通讯：英文版

Entanglement of the Common Eigenvector of Two Particles‘ Center—of—Mass Coordinate and Mass—Weighted Relative Momentum

FANHong-Yi, SUNMing-Zhai

Published Jan 1, 2002• 0 citations

OpenAlex

Abstract

Related papers

Entanglement of the Common Eigenvector of Two Particles' Center-of-Mass Coordinate and Mass-Weighted Relative Momentum

Fan Hong‐Yi, Sun Ming-zhai

We reveal that the common eigenvector of two particles' center-of-mass coordinate and mass-weighted relative momentum is an entangled state. Its Schmidt decomposition exhibits that the entanglement involves squeezing which depends on the ratio of two particles' masses. The corresponding entangling operators are derived.

Communications in Theoretical PhysicsMay 15, 20021 citation

Bipartite entangled state | $\zeta$ $\rangle$ and its applications in quantum communicationBipartite entangled state |$\zeta$$\rangle$ and its applications in quantum communication

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Bipartite entangled state |

\zeta

\rangle

and its applications in quantum communication

We give the explicit form of the common eigenstate \ensuremath{\Vert}\ensuremath{\xi}〉 of the center-of-mass coordinate ${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{Q}}_{1}

+${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{Q}}_{2}

and the mass-weighted relative momentum ${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{P}}_{1}

-${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{P}}_{2}

of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators

{\mathit{Q}}_{2}

{\mathit{Q}}_{1}

and

{\mathit{P}}_{1}

{\mathit{P}}_{2}

. The orthonormal and completeness relation of \ensuremath{\Vert}\ensuremath{\xi}〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for ${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{Q}}_{1}

+${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{Q}}_{2}

and ${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{P}}_{1}

-${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{P}}_{2}

is also derived by using the \ensuremath{\Vert}\ensuremath{\xi}〉 representation.