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Communications in Theoretical Physics

Entanglement Transfer via Heisenberg Interaction in a Four-Qubit System

Feng-Hua Ren, Zhao-Ming Wang

Published Apr 1, 2007• 3 citations
Publisher

Abstract

We investigate the entanglement transfer in a four-qubit system and calculate the concurrence between any two qubits in different initial states. We show that both the pure entangled state and mixed entangled state can be transferred. For some special coupling constants and some evolution time, entanglement can be completely transferred from one pair particles to another.

DOI
10.1088/0253-6102/47/4/010

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We investigate the entanglement transfer in a four-qubit system and calculate the concurrence between any two qubits in different initial states. We show that both the pure entangled state and mixed entangled state can be transferred. For some special coupling constants and some evolution time, entanglement can be completely transferred from one pair particles to another.
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In this paper, we consider the entanglement dynamics of a four-qubit model [2006 Phys. Rev. A 74 042328] where two entangled qubits a and b locally interact with separate qubits A and B via the spin-exchange-like Hamiltonian. We study the effect of purity of initial entangled state of qubits a, b on the entanglement evolution and its relation with energy transfer. Also, we find that the total bipartite entanglement of qubits a, b plus A, B is not a constant any longer when the initial entangled state of a, b is not pure, which is a complement to the result in the paper [2007 J. Phys. B 40 S45] for the pure case.
We consider the entanglement of two remote qubits induced by local interaction with the two-mode nonclassical state fields. We investigate the transfer of entanglement from different two-mode nonclassical state fields to a pair of separable and mixed qubits. We find that no matter what state the qubit subsystem is initially prepared in, at the specific time $gt\ensuremath{\simeq}11.07$ the entanglement of the Bell state fields can be almost completely transferred to the qubit subsystem, i.e., the Bell state fields can drive an initially separable and very mixed state of qubits into an almost pure highly entangled state suitable for quantum information processing. For the entangled coherent state fields $\ensuremath{\mid}u⟩={N}_{1}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩+\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ and $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩={N}_{2}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{-}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ we find that when $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ is small, the dynamic behaviors of the entanglement between two qubits are quite different. For $\ensuremath{\mid}u⟩$ there is almost no entanglement between two qubits while for $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩$ the dynamic behavior of the entanglement between two qubits is very similar to that of the Bell state field. For large $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ we find that the dynamic behaviors of entanglement between two qubits are almost the same for these two fields, and when $gt\ensuremath{\sim}\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}\ensuremath{\pi}$ the entanglement between two qubits reaches its maximum and is almost independent of initial mixedness of the qubit subsystem. For the two-mode squeezed vacuum state field we find that when $r\ensuremath{\sim}0.86$ and $gt\ensuremath{\simeq}11.07$ the entanglement transfer reaches its maximum which also almost does not depend on the initial mixedness of the qubit subsystem.