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Applied Mechanics and Materials

Thermal Entanglement and Dense Coding in Two-Qubit XX Spin Chain under an Arbitrary Magnetic Field

Hai Lin Huang, Zhao‐Yu Sun

Published Nov 8, 2013• 1 citation
Publisher

Abstract

The effect of arbitrary orientation in the magnetic field on the entanglement and dense coding of a two-qubit XX model is investigated. The concurrence and optimal dense coding capacity are calculated for different orientations of the magnetic field. It is found that the entanglement can be maximized by rotating the magnetic field to an optimal direction at given temperature. Furthermore, there exists critical concurrence Cc, beyond which the thermal state is unfeasible for optimal dense coding.

DOI
10.4028/www.scientific.net/amm.446-447.986

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The effect of arbitrary orientation in the magnetic field on the entanglement and dense coding of a two-qubit XX model is investigated. The concurrence and optimal dense coding capacity are calculated for different orientations of the magnetic field. It is found that the entanglement can be maximized by rotating the magnetic field to an optimal direction at given temperature. Furthermore, there exists critical concurrence Cc, beyond which the thermal state is unfeasible for optimal dense coding.
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We investigate the entanglement arising naturally in a one-dimensional Ising chain in a magnetic field in an arbitrary direction. We find that for different temperatures, different orientations of the magnetic field give maximum entanglement. In the high-temperature limit, this optimal orientation corresponds to the magnetic field being perpendicular to the Ising orientation (z(z(z direction). In the low-temperature limit, we find that varying the angle of the magnetic field very slightly from the z direction leads to a rapid rise in entanglement. We also find that the orientation of the magnetic field for maximum entanglement varies with the field amplitude. Furthermore, we have derived a simple rule for the mixing of concurrences (a measure of entanglement) due to the mixing of pure states satisfying certain conditions.
We investigate the thermal entanglement in the two-qubit Heisenberg XY model with a nonuniform magnetic field. Concurrence, the measurement of entanglement, is calculated. The behavior of concurrence is present at three different cases. Contrary to the uniform magnetic field case, we find that the entanglement and the critical temperature TC{T}_{C}TC​ may be enhanced under a nonuniform magnetic field.
We study the thermal entanglement of a 2-qutrit spin chain with nonlinear coupling in the presence of nonuniform magnetic field. Thermal entanglement of an arbitrary (finite-dimensional) m-partite system vanishes at some finite threshold temperature Ts. We investigate the dependence of Ts on the system's parameters, i.e. the nonlinear coupling and the magnetic field, for this 2-qutrit system. In addition, we compare two lower bounds of I-concurrence for this system and also study its dense coding capacity as a function of system's parameters.
We study the thermal entanglement by means of concurrence in a two-qubit isotropic XY model in the presence of site-dependent external magnetic fields in arbitrary directions. We find that at a given temperature and magnetic field strength, the mirror symmetry of the two fields about the x-y plane is a necessary condition for maximum entanglement. However, if there is no constraint on the field strengths, then the necessary condition for maximum entanglement reduces to the configuration that the two fields are vertical, anti-parallel and with the same strength. We also investigate the anisotropic XY model and find that the above conclusion more or less holds.