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arXiv:quant-ph/0505072 · International Journal of Quantum Information

CREATION OF STABLE MULTIPARTITE ENTANGLED STATES IN SPIN CHAINS WITH DEFECTS

Léa Ferreira dos Santos

Published Jun 1, 2006• 4 citations
arXivHTMLPDF

Abstract

We show how defects in a spin chain described by the XXZ model may be used to generate entangled states, such as Bell and W states, and how to maintain them with high fidelity. We also discuss, in the presence of several excitations, how the anisotropy of the system may be combined with defects to effectively assist in the creation of the desired states.

DOI
10.1142/s021974990600202x

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We investigate on how to generate maximally entangled states in systems characterized by the Hamiltonian of the XXZ\mathrm{XXZ}XXZ model with defects. Some proposed quantum computers are described by such a model. Defects embedded in this otherwise homogeneous spin chain are used to obtain Einstein-Podolsky-Rosen and W states. It is well known that a large defect localizes an excitation on the defect site. We can then consider a few identical and large defects to create a subsystem whose eigenstates are entangled. Here, we examine the cases of one and two excitations.
We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, and yielding the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50\% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes our proposal suitable for devices for rapid and robust generation of Bell states.
The transmission of quantum states in the anisotropic Heisenberg XXZ chain model with three-spin exchange interaction is studied. The average fidelity is used to evaluate the state transfer. It is found that quantum communication can be enhanced by the anisotropic coupling and multiple spin interaction. Such spin model can reduce the time required for the perfect state transmission where the fidelity is unity. The maximally entangled Bell states can be generated and separated from the whole quantum systems.
Abstract Entanglement is a crucial resource for quantum information processing, and so protocols to generate high-fidelity entangled states on various hardware platforms are in demand. While spin chains have been extensively studied to generate entanglement, graph structures also have such potential; however, only a few classes of graphs have been explored for this specific task. In this paper, we apply a particular coupling scheme involving two different coupling strengths to a graph of two interconnected 3×33\times 33×3 3 × 3 square graphs such that it effectively contains three defects. We show how this structure allows generation of a Bell state whose fidelity depends on the chosen coupling ratio. We apply partitioned graph theory in order to reduce the dimension of the graph and show that, using a reduced graph or a reduced chain, we can still simulate the same protocol with identical dynamics. Finally, we investigate how fabrication errors affect the entanglement generation protocol and how the different equivalent structures are affected, finding that for some specific coupling ratios they are extremely robust.
We study the pairwise entanglement and mixture of a three-qubit XXZ spin chain in the ground state in the presence of an external magnetic field B . The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered, and entanglement versus the mixture of all the two-spin states is investigated. We find that the maximal entangled mixed state can be obtained in the considered system by controlling the magnetic field. Our results provide another way to generate maximally entangled mixed states.
We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, which yield the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50\% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes the use of our proposed device suitable for the rapid and robust generation of Bell states in quantum information processing applications.