Skip to main content
Log in

Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian

  • Condensed Matter
  • Published:
JETP Letters Aims and scope Submit manuscript

Abstract

Entanglement is studied in an open alternating chain of nuclear spins s = 1/2 with spin-spin couplings in an external magnetic field under the thermodynamic equilibrium conditions. A reduced density matrix has been calculated for an arbitrarily chosen spin pair. The entanglement of the spin pair has been estimated according to the Wootters criterion. The temperature at which an entangled state appears in a chosen pair has been determined. It has been shown that the numerical characteristics of the entanglement are oscillating functions of the position of the spin pair in the chain.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).

    MATH  Google Scholar 

  2. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961).

    Article  MATH  ADS  Google Scholar 

  3. H. B. Cruz and L. L. Gonsalves, J. Phys. C 14, 2785 (1981).

    Article  ADS  Google Scholar 

  4. K. M. O’Connor and W. K. Wootters, Phys. Rev. A 63, 052302 (2001).

    Google Scholar 

  5. L. Amico, A. Osterloh, F. Plastina, et al., Phys. Rev. A 69, 022304 (2004).

  6. T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).

    Google Scholar 

  7. F. Meier, J. Levy, and D. Loss, Phys. Rev. Lett. 90, 047901 (2003).

  8. X. Wang, Phys. Rev. E 69, 066118 (2004).

    Google Scholar 

  9. E. B. Fel’dman and M. G. Rudavets, Pis’ma Zh. Éksp. Teor. Fiz. 81, 54 (2005) [JETP Lett. 81, 47 (2005)].

    Google Scholar 

  10. E. I. Kuznetsova and É. B. Fel’dman, Zh. Éksp. Teor. Fiz. 129, 1006 (2006) [JETP 102, 882 (2006)].

    Google Scholar 

  11. K. E. Feldman, J. Phys. A: Math. Gen. 39, 1039 (2006).

    Article  MATH  ADS  Google Scholar 

  12. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett. 92, 187902 (2004).

    Google Scholar 

  13. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).

    Article  ADS  Google Scholar 

  14. E. B. Fel’dman, R. Brüschweiler, and R. R. Emst, Chem. Phys. Lett. 294, 297 (1998).

    Article  Google Scholar 

  15. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).

    Article  ADS  Google Scholar 

  16. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, Cambridge, 1985; Mir, Moscow, 1989).

    MATH  Google Scholar 

  17. A. Abragam and M. Goldman, Nuclear Magnetism: Order and Disorder (Clarendon, Oxford, 1982; Mir, Moscow, 1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © S.I. Doronin, A.N. Pyrkov, É.B. Fel’dman, 2007, published in Pis’mav Zhurnal Éksperinental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 85, No. 10, pp. 627–631.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Doronin, S.I., Pyrkov, A.N. & Fel’dman, É.B. Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian. Jetp Lett. 85, 519–523 (2007). https://doi.org/10.1134/S0021364007100104

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364007100104

PACS numbers

Navigation