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Modern Physics Letters B

ENHANCED TELEPORTATION THROUGH ANISOTROPIC HEISENBERG QUANTUM SPIN CHAINS

Xiang Hao, Shiqun Zhu

Published Jan 9, 2008• 1 citation
Publisher

Abstract

The teleportation via the channel of the thermal equilibrium states in anisotropic Heisenberg XYZ chains is analyzed. It is found that there are the critical temperatures below which entanglement teleportation can be realized. Entanglement teleportation is enhanced through anisotropic XYZ chains in contrast to the isotropic Heisenberg one. Anisotropic spin exchanges can increase these critical temperatures for the teleportation. Entanglement can be transferred in the ferromagnetic anisotropic Heisenberg chain while it cannot be done in the ferromagnetic isotropic one. The average fidelity of the teleportation can be improved in the antiferromagnetic chains.

DOI
10.1142/s0217984908014535

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The teleportation via the channel of the thermal equilibrium states in anisotropic Heisenberg XYZ chains is analyzed. It is found that there are the critical temperatures below which entanglement teleportation can be realized. Entanglement teleportation is enhanced through anisotropic XYZ chains in contrast to the isotropic Heisenberg one. Anisotropic spin exchanges can increase these critical temperatures for the teleportation. Entanglement can be transferred in the ferromagnetic anisotropic Heisenberg chain while it cannot be done in the ferromagnetic isotropic one. The average fidelity of the teleportation can be improved in the antiferromagnetic chains.
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.
Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic.
We consider a two-qubit Heisenberg XXZ chain as a resource for quantum teleportation via the standard teleportation protocol T 0 . The effects of anisotropic on teleportation fidelity and entanglement are studied in detail. We find anisotropic not only improves the critical temperature T c and critical magnetic field B c , beyond which quantum teleportation is inferior to classical communication protocol, but also enhances the fidelity for fixed magnetic field B and temperature T. For entanglement teleportation, the effects of magnetic field on average fidelity and output entanglement are studied.
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.
Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.