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Communications in Theoretical Physics

Impurity in Pairwise Entanglement of Heisenberg XX Open Chain

Xiao-Qiang Xi, Chen Wen-xue, Qi Liu, Rui‐Hong Yue

Published Dec 1, 2007• 3 citations
Publisher

Abstract

We calculate the concurrence of all pairwise entanglement of Heisenberg XX open chain with single system impurity in three-qubit and four-qubit cases, and find that the impurity parameter J i has great effect on pairwise entanglement. Choosing the proper parameter J i , we can obtain the maximal pairwise entanglement of the nearest qubits and make the non-nearest qubits entangle.

DOI
10.1088/0253-6102/48/6/010

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We calculate the concurrence of all pairwise entanglement of Heisenberg XX open chain with single system impurity in three-qubit and four-qubit cases, and find that the impurity parameter J i has great effect on pairwise entanglement. Choosing the proper parameter J i , we can obtain the maximal pairwise entanglement of the nearest qubits and make the non-nearest qubits entangle.
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.
In this paper,we investigated the influence of impurity on the entanglement between the normal lattice in a three-qubit Ising chain.The results show that the impurity parameter has great effects on the pairwise entanglement,it can make the normal lattice disentangled and sometimes at certain regions of magnetic field B and temperature T,it can even make the concurrence between the normal lattice greater than the general pairwise entanglement of three qubits(J1=J) or two qubits(J1=0).When T=0,for the case of antiferromagnet with the conditions of θ=π/2,B→0 or θ→0,B2J,the concurrence shows a square-wave structure with the variation of the impurity parameter J1.
Basing on the calculation of all the pairwise entanglement in the nnn (n≤6n \leq 6n≤6)-qubit Heisenberg XX open chain with system impurity, we find an important result: pairwise entanglement can only be transferred through entangled pair. The non-nearest pairwise entanglement will has the possibility to exist as long as there has even number qubit in their middle. This point means that we can get longer distance entanglement in solid system.
The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature Tc decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.