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Chinese Physics B

Thermal entanglement and teleportation of a thermally mixed entangled state of a Heisenberg chain through a Werner state

Huang Li-Yuan, Mao-Fa Fang

Published Jul 1, 2008• 10 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/17/7/003

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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.
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.
This paper investigates the thermal pairwise entanglement of a three-qubit Heisenberg XXZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymmetric interaction and quantum teleportation when using the Heisenberg chain as a channel. The entanglement dependences on the DM interaction and temperature are given in detail. It obtains the relation between the concurrence and average fidelity, and shows that the same concurrence can lead different average fidelities. Moreover, it finds the thermally entangled states which do not violate the Bell inequalities, and can still be used for quantum teleportation.
Thermal pairwise entanglement of a three-qubit Heisenberg XX chain with the Dzyaloshinski-Moriya(DM) anisotropic antisymmetric interaction under an external magnetic field and quantum teleportation when using the Heisenberg chain as a channel are investigated.The entanglement and fidelity depending on the DM interaction,magnetic field and temperature are given in detail.The results show that the thermal entanglement can be controlled by magnetic field and DM interaction.Quantum teleportation will be better realized via an ferromagnetic spinchain when the DM interaction and external magnetic field are turned off and the temperature is low.The thermal entanglement cannot completely reflect the teleportation fidelity,and the same thermal entanglement could yield different average teleportation fidelities.
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.
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.
We study the optimal teleportation based on Bell measurements via the thermal states of a two-qubit Heisenberg XXX chain in the presence of the Dzyaloshinsky-Moriya (DM) anisotropic antisymmetric interaction and obtain an optimal unitary transformation. The explicit expressions of the output state and the teleportation fidelity are presented and compared with those of the standard protocol. It is shown that in this protocol the teleportation fidelity is always larger and the unit fidelity is achieved at zero temperature. The DM interaction can enhance the teleportation fidelity at finite temperatures, as opposed to the effect of the interaction in the standard protocol. Cases with other types of anisotropies are also discussed.