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Communications in Theoretical Physics

Entanglement and Teleportation via Thermally Entangled State of Anisotropic Heisenberg XYZ Chain with Inhomogeneous External Magnetic Field

Ni Hui-Ying, Fang Jian-Xing, Zhu Shi-Qun, Sha Jin-Qiao, Jiang Wei-Xing

Published Feb 1, 2008• 1 citation
Publisher

Abstract

In this paper we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component JZ, the inhomogeneous magnetic field b, the anisotropy ?, and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fa. High average fidelity of the teleportation is obtained when the temperat ure is very low. Under some condition, we also find that when inhomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.

DOI
10.1088/0253-6102/49/2/17

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In this paper we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component JZ, the inhomogeneous magnetic field b, the anisotropy ?, and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fa. High average fidelity of the teleportation is obtained when the temperat ure is very low. Under some condition, we also find that when inhomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.
This paper studies the average fidelity of teleportation and thermal entanglement for a two-qubit Heisenberg XYZ chain in the presence of both an inhomogeneous magnetic field and a Dzyaloshinski–Moriya interaction. It shows that for a fixed D z , the increase of b z will broaden the critical temperature at the cost of decreasing the thermal entanglement. And it can modulate the inhomogeneous magnetic field and the Dzyaloshinski–Moriya interaction for the average fidelity of teleportation to be optimal.
In the experiment of quantum communication,maximal entangled pure states are difficult to got due to the effects of environment.Therefore,a quantum channel is always represented by a form of mixed states.The thermal equilibrium state in solid state materials is one essential mixed entangled state.In this dissertation,a two-particle entangled state can be teleported through the channel of thermal mixed states in two independent 1D Heisenberg chains.We study the effects of the non-uniform external magnetic field B and temperature T on the entanglement and fidelity.In order to characterize the quality of the teleported state,we make a research of the average fidelity FA.And when B1 and B2 have different directions,the entanglement teleportation is better than the classical teleportation under low temperature.At that case the average fidelity is always larger than 2/3 which is the limited value of the classical teleportation.
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.
Quantum teleportation via the entanglement channel composed of a two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interaction in the presence of both inhomogeneous external magnetic field and intrinsic decoherence has been investigated. It is shown that the initial state of the channel plays an important role in the fully entangled fraction and the average fidelity of teleportation. It is found that when the initial system is in the entangled state |Ψ⟩ = m2|01⟩ + n2|10⟩ the corresponding average fidelity is always larger than 2/3.