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Journal of Yanbian University

Pairwise Entanglement in the Four-qubit Heisenberg XX Open Chain

Wanqiang Cao

Published Jan 1, 2009• 0 citations
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Abstract

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.

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Journal of Yanbian University•Jan 1, 2009•0 citations
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.
The concurrence of two alternate qubits in a four-qubit Heisenberg XXXXXX chain is investigated when a uniform magnetic field BBB is included. It is found that there is no thermal entanglement between alternate qubits if BBB is close to zero. A magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic cases. Near zero temperature, the entanglement undergoes two sudden changes with increasing value of the magnetic field BBB. This is due to the changes in the ground state. This novel property may be used as a quantum entanglement switch. The anisotropy in the system can also induce the entanglement between two alternate qubits.
For a three-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modelling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.