Entanglement and Fidelity of Quantum Teleportation in Heisenberg XXZ Model with Multiple Interactions

Document Type : Full length research Paper

Author

Department of Physics, Sahand University of Technology, Sahand New Town, Tabriz, Iran

Abstract

In this paper, we considered the two-qubit Heisenberg XXZ model with Dzyaloshinski-Moriya (DM) interaction under the Calogero-Moser model type I, where each spin is affected by the homogeneous and inhomogeneous magnetic field. Assuming that the initial state of the system is , we examined the effects of the relative distance between spins, intrinsic decoherence, magnetic field, DM interaction and the parameters of the initial state of the system on the dynamics of quantum entanglement. The results showed that by increasing the relative distance between the spins, the entanglement decreased. In addition, by applying the inhomogeneous magnetic field in the presence of DM interaction, the effect of intrinsic decoherence on entanglement dynamics could be observed. We also used the two-qubit Heisenberg XXZ model density matrix in the presence of intrinsic decoherence as a quantum channel to teleport the quantum states from the sender to the receiver. Using the fidelity measure, we studied the effect of the different parameters on the quality of the teleported quantum state. We observed that by applying the inhomogeneous magnetic field and in the presence of the DM interaction, the average fidelity is larger than the minimum of the average fidelity i.e.,  

Keywords

Main Subjects

References

[1] A. Einstein, B. Podolski, N. Rosen, Can quantum mechanical description of physical reality be considered complete?, Physical Review 47 (1935) 777-780. https://doi.org/10.1103/PhysRev.47.777
[2] C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Physical Review Letter 70 (1993) 1895–1899. https://doi.org/10.1103/PhysRevLett.70.1895
[3] R. Jozsa, Fidelity for mixed quantum states, Journal of modern optics 41 (1994) 2315-2323. https://doi.org/10.1080/09500349414552171
[4] G. Burkard, D. Loss, D.P. Divincenzo, Coupled quantum dots as quantum gates, Physical Review B 59 (1999) 2070. https://doi.org/10.1103/PhysRevB.59.2070[5] R. Vrijen, et al., Electron-spin-resonance transistors for quantum computing in silicon germanium heterostructures, Physical Review A 62 (2000) 012306. https://doi.org/10.1103/PhysRevA.62.012306[6] S. Bose, Quantum communication through an unmodulated spin chain, Physical review letters 91 (2003) 207901. https://doi.org/10.1103/PhysRevLett.91.207901[7] M. Christandl, N. Datta, A. Ekert, A.J. Landahl, Perfect state transfer in quantum spin networks, Physical review letters 92 (2004) 187902. https://doi.org/10.1103/PhysRevLett.92.187902

[8] G.J. Milburn, Intrinsic decoherence in quantum mechanics, Physical Review A 44 (1991) 5401. https://doi.org/10.1103/PhysRevA.44.5401

[9] S.B. Li, J.B. Xu, Magnetic impurity effects on the entanglement of three-qubit Heisenberg XY chain with intrinsic decoherence, Physics Letters A 334 (2005) 109-116. https://doi.org/10.1016/j.physleta.2004.11.008[10] B. Shao, T.H. Zeng, J. Zou, Influence of intrinsic decoherence on entanglement in two-qubit quantum Heisenberg XYZ chain, Communications in Theoretical Physics 44 (2005) 255. https://doi.org/10.1088/6102/44/2/255[11] Z. He, Z. Xiong, Y. Zhang, Influence of intrinsic decoherence on quantum teleportation via two-qubit Heisenberg XYZ chain, Physics Letters A 354 (2006) 79-83. https://doi.org/10.1016/j.physleta.2006.01.038[12] X.B. Xu, J.M. Liu, P.F. Yu, Entanglement of a two-qubit anisotropic Heisenberg XYZ chain in nonuniform magnetic fields with intrinsic decoherence, Chinese Physics B 17 (2008) 456. https://doi.org/10.1088/1674-1056/17/2/019[13] J.L. Guo, Y. Xia, H.S. Song, Effects of Dzyaloshinski-Moriya anisotropic antisymmetric interaction on entanglement and teleportation in a two-qubit Heisenberg chain with intrinsic decoherence, Optics communications 281 (2008) 2326-2330. https://doi.org/10.1016/j.optcom.2007.11.082[14] K. Hikami, M. Wadati, Integrability of Calogero-Moser spin system, Journal of the Physical Society of Japan 62 (1993) 469-472. https://doi.org/10.1143/JPSJ.62.469
[15] W.K. Wootters, Entanglement Formation of an Arbitrary State of Two Qubits, Physical Review Letter 80 (1998) 22-45. https://doi.org/10.1103/PhysRevLett.80.2245
[16] W.K. Wootters, Entanglement of formation and concurrence, Quantum Information and Computation 1 (2001) 27- 44. https://doi.org/10.26421/QIC1.1-3
Journal of Research on Many-body Systems
Volume 12, Issue 3 - Serial Number 34
autumn 2022
December 2022
Pages 39-49

Files

History

  • Receive Date: 30 December 2021
  • Revise Date: 27 April 2022
  • Accept Date: 01 October 2022

Share

How to cite

Statistics