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Acta Sinica Quantum Optica

Quantum Teleportation through the Channel of Thermal Mixed States in Two Independent Heisenberg Chains

Fang Jian-Xing

Published Jan 1, 2009• 0 citations
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Abstract

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.

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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.
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.
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.
The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski–Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of the noisy quantum channel are studied in detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.
This study investigates thermal entanglement in a four-qubit spin chain of Heisenberg model XX with the presence of the Dzyaloshinski-Moriya (DM) anisotropic asymmetric interaction, an external magnetic field, and another parameter. Then, the spin chain was used as a quantum channel for transferring an unknown quantum state. Finally, fidelity concept was used to check the similarity between input state and output state which, in fact, shows the degree of success in teleportation. In this way, the effect of different parameters on the fidelity was determined. It was concluded that quantum channel comprised of four-qubit spin chain which has thermal equilibrium is an appropriate candidate for quantum transfer of information.
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.