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arXiv:quant-ph/0302101 · Physical Review A

Studying the thermally entangled state of a three-qubit HeisenbergXXring via quantum teleportation

Ye Yeo

Published Aug 27, 2003• 47 citations
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Abstract

We consider quantum teleportation as a tool to investigate the thermally entangled state of a three-qubit Heisenberg $\mathrm{XX}$ ring. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence of the state. In particular, two mixtures of different pairs of W states, which result in the same concurrence, could yield very different average teleportation fidelities.

DOI
10.1103/physreva.68.022316

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We consider quantum teleportation as a tool to investigate the thermally entangled state of a three-qubit Heisenberg XX\mathrm{XX}XX ring. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence of the state. In particular, two mixtures of different pairs of W states, which result in the same concurrence, could yield very different average teleportation fidelities.
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.
In this paper, we consider the generation of a three-qubit Greenberger-Horne-Zeilinger-like thermal state by applying the entanglement swapping scheme of Zukowski et al. [Ann. N. Y. Acad. Sci. 755, 91 (1995)] to three pairs of two-qubit Heisenberg XYXYXY chains. The quality of the resulting three-qubit entanglement is studied by analyzing the teleportation fidelity, when it is used as a resource in the teleportation protocol of Karlsson et al. [Phys. Rev. A 58, 4394 (1998)]. We show that even though thermal noise in the original two-qubit states is amplified by the entanglement swapping process, we are still able to achieve nonclassical fidelities for the anisotropic Heisenberg XYXYXY chains at finitely higher and higher temperatures by adjusting the strengths of an external magnetic field. This has a positive implication on the solid-state realization of a quantum computer.