mriselMagnetic Resonance in SolidsMagnetic Resonance in Solids2072-5981Kazan Federal Universitymrisel-203Research ArticleСтатьиEntanglement in One-Dimensional Open Chains of Spins 1/2 with XY-HamiltonianDoroninS. I.

142432, Chernogolovka

Fel'dmanE. B.

142432, Chernogolovka

PyrkovA. N.

142432, Chernogolovka

pyrkov@icp.ac.ruInstitute of Problems of Chemical Physics of RASRussian Federation200621012024813337Copyright © Doronin S.I., Fel'dman E.B., Pyrkov A.N., 20242024Doronin S.I., Fel'dman E.B., Pyrkov A.N.Doronin S.I., Fel'dman E.B., Pyrkov A.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mrsej.ru/jour/article/view/203

We investigate entanglement of spin pairs in a one-dimension open chain of spins coupled by the dipole-dipole interactions (DDI) in the equilibrium state in the external magnetic field. We suggest a method of calculation of the reduced density matrix. Concurrence, the quantitative measure of the entanglement, is estimated with Wootter's criteria. Analytical and numerical methods are used in order to investigate the influence of the temperature, chain's length, distance between the spins and their distance from the chain's ends on their entanglement.

XY-Hamiltonianmagnetic resonancereduced density matrixquantum registerquantum computingentanglementqubitaddressing problemThis work was supported by the Russian Foundation for Basic Research (project no. 04-03-32528).ReferencesShor P.W. in Proceedings of the Symposium on the Foundations of Computer Science, 1994, pp. 124-134.Shor P.W. in Proceedings of the Symposium on the Foundations of Computer Science, 1994, pp. 124-134.Grover L.K. Phys. Rev. Lett. 79, 325-328 (1997).Grover L.K. Phys. Rev. Lett. 79, 325-328 (1997).Nielsen M. and Chuang I. Quantum Computation and Quantum Communication, Cambridge, 2000.Nielsen M. and Chuang I. Quantum Computation and Quantum Communication, Cambridge, 2000.Wootters W.K. Phys. Rev. Lett. 80, 2245 (1998).Wootters W.K. Phys. Rev. Lett. 80, 2245 (1998).Lieb E.H., Schultz T., Mattis D. Ann. Phys. (Paris) 16 (1961) 407.Lieb E.H., Schultz T., Mattis D. Ann. Phys. (Paris) 16 (1961) 407.Fel’dman E.B., Bruschweiler R., Ernst. R.R. Chem. Phys. Lett. 294, 297 (1998).Fel’dman E.B., Bruschweiler R., Ernst. R.R. Chem. Phys. Lett. 294, 297 (1998).Fel’dman E.B., and Rudavets M.G. JETP Letters, 81, 47 (2005).Fel’dman E.B., and Rudavets M.G. JETP Letters, 81, 47 (2005).Kuznetsova E.I., Fel’dman E.B. JETP 102, 882 (2006).Kuznetsova E.I., Fel’dman E.B. JETP 102, 882 (2006).Amico L., Osterloh A., Plastina F., Fazio R., Palma G.M. Phys. Rev. A. 69, 022304 (2004).Amico L., Osterloh A., Plastina F., Fazio R., Palma G.M. Phys. Rev. A. 69, 022304 (2004).Osborne T.J. and Nielsen M.A. Phys. Rev. A. 66, 032110 (2002).Osborne T.J. and Nielsen M.A. Phys. Rev. A. 66, 032110 (2002).Wang X. Phys. Rev. E. 69, 066118 (2004).Wang X. Phys. Rev. E. 69, 066118 (2004).Abragam A. and Goldman M. Nuclear Magnetism: Order and Disorder. Oxford, England: Oxford University Press, 1982.Abragam A. and Goldman M. Nuclear Magnetism: Order and Disorder. Oxford, England: Oxford University Press, 1982.

The authors declare that there are no conflicts of interest present.