Influence of nonlinear interaction on the quantum entanglement and fidelity under intrinsic decoherence

Abstract

Abstract: Using the Milburn equation, we have studied the properties of the entanglement and fidelity dynamics in a Heisenberg spin model with nonlinear coupling. The effects of nonlinear coupling and the initial states on the quantum entanglement and the average fidelity are discussed. Results show that the conditions for system in ferromagnetic or antiferromagnetic will have significant impact on the result of entanglement versus nonlinear coupling. Moreover, we find that the behavior of average fidelity is affected by the initial state, so the initial state is one of the significant factors to determine what kinds of system are suitable as quantum channel.

Key words: quantum optics; entanglement; nonlinear coupling; intrinsic decoherence

CLC Number:

O413.1

WANG Xiao, QIN Meng. Influence of nonlinear interaction on the quantum entanglement and fidelity under intrinsic decoherence[J]. J4, 2016, 33(5): 561-565.

References

[1] Zhang Yongde. Principles of quantum information physics. [M] 北京：科学出版社，2006.
[2] Einstein A, Podolsky B, Rosen N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? [J] Phys. Rev., 1935, 47:777.
[3] Imamoglu A, Awschalom D D, Burkard G. Quantum Information Processing Using Quantum Dot Spins and Cavity QED [J]. Phys. Rev. Lett, 1999, 83: 4204-4207.
[4] Su Xiaoqin, Guo Guangcan. Quantum communication and quantum computation. [J]. Chinese Journal of Quantum Electronics (量子电子学报), 2004，21 (6) ：706-718 (in Chinese).
[5] Bose S. Quantum Communication through an Unmodulated Spin Chain [J]. Phys Rev Lett, 2003, 91: 207901.
[6] Horodecki R, Horodecki P, Horodecki M, Horodecki K, Quantum entanglement [J]. Rev. Mod. Phys. 2009, 81, 865.
[7] Amico L, Fazio R, Osterloh A, Vedral V, Entanglement in many-body system [J]. Rev. Mod. Phys. 2008, 80, 517.
[8] Arnesen M C, Bose S, Vedral V. Natural Thermal and Magnetic Entanglement in the 1D Heisenberg Model [J]. Phys. Rev. Lett, 2001, 87:017901.
[9] Cao Min, Zhu Shiqun. Thermal entanglement between alternate qubits of a four-qubit Heisenberg XX chain in a magnetic field [J]. Phys. Rev. A 2005, 71, 034311.
[10] Zhang Rong, Zhu Shiqun. Thermal entanglement in a two-dimensional Heisenberg XY model [J]. Phys. Lett. A, 2006, 348: 110-118.
[11] Zhang Guofeng, Li Shushen. Entanglement in a spin-one chain [J]. Solid. State. Communications, 2006, 138:17
[12] Qin Meng, Tao Yingjuan. Hu Mingliang, Tian Dongping. Entanglement in spin-1 Heisenberg XXZ chain[J]. Chinese Journal of Quantum Electronics (量子电子学报), 2008, 25(3): 302-306 (in Chinese).
[13] Zhang Guo Feng, Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction. [J]. Phys. Rev. A 2007, 75: 034304.
[14] Li Da Chuang, Cao Zhuo Liang, Entanglement in the anisotropic Heisenberg XYZ model with different Dzyaloshinskii-Moriya interaction and inhomogeneous magnetic field. [J]. Eur. Phys. J. D 2008, 50:207.
[15] Wootters W K, Entanglement of formation of an arbitrary state of two qubits [J].Phys. Rev. Lett. 1998, 80:2245.
[16] Hill S, Wootters W K, Entanglement of a pair of quantum bits [J]. Phys. Rev. Lett. 1997, 78: 5022.
[17] Lee J, Kim M S, Entanglement teleportation via Werner states [J]. Phys. Rev. Lett. 2000, 84, 4236.
[18] Jozsa R, Fidelity for mixed quantum states [J]. J. Mod. Opt. 1994, 41, 2315-2323.
[19] Milburn G J, Intrinsic decoherence in quantum mechanics[J]. Phys. Rev. A 1991, 44, 5401–5406.