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arXiv:quant-ph/9912061

Teleportation of entanglement for continuous variables

В. Н. Горбачев, Andrew I. Trubilko

Published Dec 13, 1999• 1 citation
arXivHTMLPDF

Abstract

Teleportation of a pure two particle entangled state of continuous variables by triplet of the Greenberger-Horne-Zeilinger form is considered. The three-particle basis needed for a joint measurement is found. It describes a measurement of momentum one of single particle and total moment and relative position of the two others. Optical realization using squeezed state of the light is discussed.

DOI
10.48550/arxiv.quant-ph/9912061

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Teleportation of a pure two particle entangled state of continuous variables by triplet of the Greenberger-Horne-Zeilinger form is considered. The three-particle basis needed for a joint measurement is found. It describes a measurement of momentum one of single particle and total moment and relative position of the two others. Optical realization using squeezed state of the light is discussed.
The teleportation of a two-particle entangled state, using a Greenberger-Horne-Zeilinger triplet, for continuous variables is studied. The basis for joint three-particle measurements is found, where the vectors describe the states in which only two of three particles are entangled. It represents the measurement of the momentum of one particle and the difference of coordinates and the sum of momenta of the two other particles. An optical realization of this scheme is presented, which uses squeezed states of light and reduces the measurement of momentum and coordinate to the detection of quadrature operators of the electromagnetic field.
Teleportation of some pure entangled states of discrete and continuous variables is considered using a multi-particle quantum channel; particularly a Greenberger-Horne-Zeilinger channel. Both the protocols we have found for the discrete and continuous versions have identical features due to the properties of the quantum channel. In this way some entangled states can be teleported perfectly; a non-Bell-state measurement is needed in contrast to the one-by-one protocol where an unknown state can be recovered by all receivers only. For teleportation of continuous variables an optical implementation using squeezed light states is discussed.
A controlled quantum teleportation of continuous variable using a tripartite Greenberger–Horne–Zeilinger (GHZ) state is proposed. The protocol enables controlling the fidelity of bipartite teleportation by shifting the phase of one of the three modes involved in the teleportation. This method reduces the quality of the tripartite entanglement and by quadrature measurements of the changed mode, bipartite entanglement can be distilled from the original entanglement. Because of the phase shift, the quality of the bipartite entanglement is inferior to the entanglement distilled from the original GHZ-state. By controlling the quality of the entanglement we realize the controlled teleportation.