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.
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References
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).
E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961).
H. B. Cruz and L. L. Gonsalves, J. Phys. C 14, 2785 (1981).
K. M. O’Connor and W. K. Wootters, Phys. Rev. A 63, 052302 (2001).
L. Amico, A. Osterloh, F. Plastina, et al., Phys. Rev. A 69, 022304 (2004).
T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).
F. Meier, J. Levy, and D. Loss, Phys. Rev. Lett. 90, 047901 (2003).
X. Wang, Phys. Rev. E 69, 066118 (2004).
E. B. Fel’dman and M. G. Rudavets, Pis’ma Zh. Éksp. Teor. Fiz. 81, 54 (2005) [JETP Lett. 81, 47 (2005)].
E. I. Kuznetsova and É. B. Fel’dman, Zh. Éksp. Teor. Fiz. 129, 1006 (2006) [JETP 102, 882 (2006)].
K. E. Feldman, J. Phys. A: Math. Gen. 39, 1039 (2006).
M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett. 92, 187902 (2004).
W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
E. B. Fel’dman, R. Brüschweiler, and R. R. Emst, Chem. Phys. Lett. 294, 297 (1998).
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, Cambridge, 1985; Mir, Moscow, 1989).
A. Abragam and M. Goldman, Nuclear Magnetism: Order and Disorder (Clarendon, Oxford, 1982; Mir, Moscow, 1984).
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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.
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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
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DOI: https://doi.org/10.1134/S0021364007100104