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Acta Sinica Quantum Optica

Research on the Quantum Teleportation in Heisenberg Model

Xueming Qian

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

In this paper, we study quantum entanglement in Heisenberg model in the first; with that, the quantum teleportation via Heisenberg thermally entangled state is studied also. And then the concurrence and the fidelity are calculated. Finally the entanglement teleportation interacting with exoteric environment is analysed.

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The thermal entanglement of a two-qubit XXZ Heisenberg model in the presence of Dzyaloshinski-Moriya anisotropic antisymmetric interaction in a homogeneous magnetic field is studied,and this model is used as the quantum channel to teleport a two-qubit pure state,then the entanglement of teleported state and the average fidelity of teleportation are calculated.Finally the influences on the entanglement of outper states and average fidelity in terms of the D-M coupling constant,spin coupling constant,anisotropy parameter,magnetic induction and temperature are discussed.
Entanglement teleportation, using thermally entangled state of two two-qubit Heisenberg XX chain as resource, was carried out. The deferent density operator and the fidelity of teleportation were calculated. And then, how the entanglement teleportation depends on the temperature and the magnetic field was analyzed. The results show that the entanglement teleportation of the mixed quantum channel is superior to the classical communication when the magnetic field B is feebleness and the temperature T is very low.
Natural thermal entanglement between two qubits with XXX Heisenberg interaction is studied. For the antiferromagnet, increasing coupling strength or decreasing temperature under critical point increases the entanglement. Based on the thermal entanglement as quantum channel, entanglement and information of an input entangled state are transferred via partial teleportation. We find that the entanglement transferred will be lost during the process, and for the entanglement fidelity the partial teleportation is superior to classical communication as concurrence of entangled channel beyond 1/4. We show that both correlation information in input entangled state and individual information of the teleported particle are linearly dissipated. With more entanglement in quantum channel, more entanglement and correlation information can be transferred.
The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field. The effects of the anisotropy and magnetic field for the quantum fidelity are studied in detail. The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obtained. We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity. The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation.