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Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments

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Abstract

Quantum correlations are investigated theoretically in a two-spin system with the dipole–dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of \(\pi /2\)-pulses only and the delays between the pulses can differ. The second scheme contains \(\varphi \)-pulses (\(0<\varphi <\pi \)) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between \(\pi /2\)-pulses at arbitrary temperatures. Entanglement emerges after several periods of the pulse sequence in the second scheme at \(\varphi =\pi /4\) at milliKelvin temperatures. The necessary number of the periods increases with increasing temperature. We demonstrate the dependence of entanglement on the number of the periods of the multiple-pulse sequence. Quantum discord is obtained for the first scheme of the multiple-pulse spin-locking experiment at different temperatures.

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References

  1. Haeberlen, U.: Multiple pulse techniques in solid state NMR. Magn. Res. Rev. 10, 81 (1985)

    Google Scholar 

  2. Ostroff, E.D., Waugh, J.S.: Multiple spin echoes and spin locking in solids. Phys. Rev. Lett. 16, 1097 (1966)

    Article  ADS  Google Scholar 

  3. Mansfield, P.D., Ware, D.: Nuclear resonance line narrowing in solids by repeated short pulse r. f. irradiation. Phys. Lett. 22, 133 (1966)

    Article  ADS  Google Scholar 

  4. Ernst H., Fenzke D., Heink W.: Damping of Multiple Spin Echoes in Solids. First Specialized Collîque AMPERE. Krakow, Institute of Nuclear Physics, 122 (1973)

  5. Yerofeev, L.N., Shumm, B.A., Manelis, G.B.: Nuclear magnetization relaxation in a multipulse NMR experiment. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 75(5), 1837 (1978)

    Google Scholar 

  6. Ivanov, Y.N., Provotorov, B.N., Feldman, E.B.: Thermodynamic theory of NMR spectral-line narrowing in solids. Zhurnal Experimentalnoi i Theoreticheskoi Fiziki 75(5), 1847 (1978)

    Google Scholar 

  7. Kuznetsova, E.I., Fel’dman, E.B., Feldman, D.E.: Magnus expansion paradoxes in the study of equilibrium magnetization and entanglement in multi-pulse spin locking. Physics-Uspekhi 59, 577 (2016)

    Article  ADS  Google Scholar 

  8. Fel’dman, E.B., Feldman, D.E., Kuznetsova, E.I.: Floquet Hamiltonian and entanglement in spin systems in periodic magnetic fields. Appl. Magn. Reson. 48, 517 (2017)

    Article  Google Scholar 

  9. Goldman, M.: Spin Temperature and Nuclear Magnetic Resonance in Solids. Chapters 1, 2. Clarendon Press, Oxford (1970)

    Google Scholar 

  10. Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  11. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  MATH  Google Scholar 

  12. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  13. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34, 6899 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  15. Fel’dman, E.B., Kuznetsova, E.I., Yurishchev, M.A.: Quantum correlations in a system of nuclear \(s=1/2\) spins in a strong magnetic field. J. Phys. A Math. Theor. 45, 475304 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Abragam, A., Goldman, M.: Nuclear Megnetism: Order and Disorder. Chapter 8. Clarendon Press, Oxford (1982)

    Google Scholar 

  17. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

  18. Bennet, C.H., DiVincenzo, D.P., Fuchs, C.A.: Quantum nonlocality without entanglement. Phys. Rev A 59, 1070 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  19. Braunstein, S.L., Caves, C.M., Jozca, R., Linden, N., Popescu, S., Schack, R.: Separability of very noisy mixed states and implication for NMR quantum computing. Phys. Rev. Lett. 83, 1054 (1999)

    Article  ADS  Google Scholar 

  20. Meyer, D.A.: Sophisticated quantum search without entanglement. Phys. Rev. Lett. 85, 2014 (2000)

    Article  ADS  Google Scholar 

  21. Bera A., Das T., Sadhukhan D., Roy S. S., Sen(De) A., Sen U.: Quantum Discord and its allies: a review of recent progress. Reports on Progress in Physics accepted, https://doi.org/10.1088/1361-6633/aa872f

  22. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  23. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  24. Doronin, S.I., Fel’dman, E.B., Kuznetsova, E.I.: Contributions of different parts of spin-spin interactions to quantum correlations in a spin ring model in an external magnetic field. Quantum Inf. Process. 14, 2929 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Yurishchev, M.A.: NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore. JETP 119, 828 (2014)

    Article  ADS  Google Scholar 

  26. Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 52107 (2010)

    Article  ADS  Google Scholar 

  27. Ciliberti, L., Rossignoli, R., Canosa, N.: Quantum discord in finite XY chains. Phys. Rev. A 82, 042316 (2010)

    Article  ADS  MATH  Google Scholar 

  28. Chernyavskiy A. Y.: Calculation of quantum discord and entanglement measures using the random mutations optimization algorithm. arXiv:1304.3703

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Acknowledgements

The work is supported by Russian Foundation of Basic Research (Grant No. 16-03-00056) and the Program of the Presidium of the Russian Academy of Sciences No. 5 “Electron spin resonance, spin-dependent electron effects and spin technologies”.

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Authors and Affiliations

  1. Faculty of Fundamental Physical-Chemical Engineering, Lomonosov Moscow State University, GSP-1, Moscow, Russia, 119991

    S. A. Gerasev

  2. Institute of Problems of Chemical Physics of Russian Academy of Sciences, Chernogolovka, Moscow Region, Russia, 142432

    S. A. Gerasev, A. V. Fedorova, E. B. Fel’dman & E. I. Kuznetsova

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  1. S. A. Gerasev
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  2. A. V. Fedorova
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  3. E. B. Fel’dman
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  4. E. I. Kuznetsova
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Correspondence to A. V. Fedorova.

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Gerasev, S.A., Fedorova, A.V., Fel’dman, E.B. et al. Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments. Quantum Inf Process 17, 72 (2018). https://doi.org/10.1007/s11128-018-1841-x

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