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Journal of Modern Optics

Dynamics of pairwise entanglement in the four-qubit HeisenbergXXspin chain

Jin‐Liang Guo, He‐Shan Song

Published Oct 10, 2008• 2 citations
Publisher

Abstract

We discuss the dynamic evolution of pairwise entanglement in a four-qubit Heisenberg XX spin chain with the periodic boundary condition and the external magnetic field considered. The results show that the so-called entanglement sudden death (ESD) effect can be weakened when introducing the periodic boundary condition and the magnetic impurity. In addition, we also find that the ESD affects the dynamic evolution of entanglement between weakly interacting alternate qubits stronger than that for strongly interacting nearest qubits.

DOI
10.1080/09500340802167532

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We discuss the dynamic evolution of pairwise entanglement in a four-qubit Heisenberg XX spin chain with the periodic boundary condition and the external magnetic field considered. The results show that the so-called entanglement sudden death (ESD) effect can be weakened when introducing the periodic boundary condition and the magnetic impurity. In addition, we also find that the ESD affects the dynamic evolution of entanglement between weakly interacting alternate qubits stronger than that for strongly interacting nearest qubits.
For a three-qubit Heisenberg XX spin chain with the uniform magnetic field and magnetic impurity, dynamic evolution of pairwise entanglement are studied. We show that the phenomenon of entanglement sudden death (ESD) occurs in the evolution of entanglement for some initial states. We also find that magnetic impurity cannot only eliminate the phenomenon of ESD but also induce the ESD effects, which is different from the case of uniform magnetic field where the ESD can be depressed but cannot be eliminated by introducing the uniform magnetic field.
We investigate the effects of anisotropy on the dynamic evolution of pairwise entanglement in the four-qubit Heisenberg XXZ model. The entanglement between the nearest-neighbor and the next nearest-neighbor qubits are calculated by making use of concurrence. Our results show that the sudden death effect can be weakened when introducing the anisotropy Δ. In addition, we also find that the anisotropy Δ can protect the entanglement between the nearest-neighbor qubits from being completely destroyed by the intrinsic decoherence, but it cannot do this for the entanglement between the next nearest-neighbor qubits.
The pairwise entanglement in the four-qubit Heisenberg XX open chain with external magnetic fields is calculated,and the analytical expressions for the measures of entanglement Concurrence are obtained.It is found that the entanglement between the boundary qubits can reach the value of 0.28 in the system with uniform external magnetic fields.In addition,in the Heisenberg XX model with external magnetic fields on the two boundary qubits,the two non-boundary qubits will be in the maximal entanglement by increasing the magnetic field at low temperature.
Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic Geld. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic Geld and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic Geld, and the coupling strength with their environment. In particular, we Gnd that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.
In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii–Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.