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Herring–Flicker coupling and thermal quantum correlations in bipartite system

  • Kapil K. Sharma
Article
  • 103 Downloads

Abstract

In this paper, we study thermal quantum correlations as quantum discord and entanglement in bipartite system imposed by external magnetic field with Herring–Flicker coupling, i.e., \(J(R)=1.642 e^{-2 R} R^{5/2}+O(R^{2}e^{-2R})\). The Herring–Flicker coupling strength is the function of R, which is the distance between spins and systems carry XXX Heisenberg interaction. By tuning the coupling distance R, temperature and magnetic field quantum correlations can be scaled in the bipartite system. We find the long sustainable behavior of quantum discord in comparison with entanglement over the coupling distance R. We also investigate the situations, where entanglement totally dies but quantum discord exists in the system.

Keywords

Herring–Flicker coupling Quantum discord Thermal entanglement Bipartite spin system 

Notes

Acknowledgements

The authors acknowledge support from the Ministry of Electronics & Information Technology, Government of India, through the Centre of Excellence in Nano-Electronics, IIT Bombay.

References

  1. 1.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRefGoogle Scholar
  2. 2.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  3. 3.
    Bose, S., Bayat, A., Sodano, P., Banchi, L., Verrucchi, P.: Spin Chains as Data Buses, Logic Buses and Entanglers, Chapter: Quantum State Transfer and Network Engineering, pp. 1–37 (2013)Google Scholar
  4. 4.
    D’Amico, I.: Quantum dot-based quantum buses for quantum computer hardware architecture. Microelectron. J. 37, 1440 (2006)CrossRefGoogle Scholar
  5. 5.
    Schirmer, S.G., Pemberton-Ross, P.J.: Fast high fidelity information transmission through spin chain quantum wires. Phys. Rev. A 80, 030301 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    Haldane, F.D.M.: Exact Jastrow–Gutzwiller resonating-valence-bond ground state of the spin 1/2 antiferromagnetic Heisenberg chain with \(\frac{1}{r^{2}}\) exchange. Phys. Rev. Lett. 60, 635 (1988)ADSCrossRefGoogle Scholar
  7. 7.
    Shastry, B.S.: Exact solution of an S=\(\frac{1}{2}\) Heisenberg antiferromagnetic chain with long-ranged interactions. Phys. Rev. Lett. 60, 639 (1988)ADSCrossRefGoogle Scholar
  8. 8.
    Lin, B., Wang, Y.S.: Quantum correlations in a long range interaction spin chain. Phys. B 407, 77 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    XiaoSan, M., Ying, Q., GuangXing, Z., AnMin, W.: Quantum discord of thermal states of a spin chain with Calogero–Moser type interaction. Sci. China 56, 600 (2013)Google Scholar
  10. 10.
    Bravo, B., Cabra, D.C., Gmez Albarracn, F.A., Rossini, G.L.: Long-range interactions in antiferromagnetic quantum spin chains. Phys. Rev. B 96, 054441 (2017)ADSCrossRefGoogle Scholar
  11. 11.
    Homrighausen, I., Abeling, N.O., Zauner-Stauber, V., Halimeh, J.C.: Anomalous dynamical phase in quantum spin chains with long-range interactions. Phys. Rev. B 96, 104436 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    Neyenhuis, B., Zhang, J., Hess, P.W., Smith, J., Lee, A.C., Richerme, P., Gong, Z.X., Gorshkov, A.: Observation of prethermalization in long-range interacting spin chains. Sci. Adv. 3(8), e1700672 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    Hunga, C.L., Gonzlez-Tudelac, A., Ignacio, C.J., Kimble, H.J.: Quantum spin dynamics with pairwise-tunable long-range interactions. PNAS 113, 34 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Herring, C., Flicker, M.: Asymptotic exchange coupling of two hydrogen atoms. Phys. Rev. 134, A362 (1964)ADSCrossRefGoogle Scholar
  15. 15.
    Huang, Z., Kais, S.: Entanglement as measure of electron–electron correlation in quantum chemistry calculations. Chem. Phys. Lett. 413, 1 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Kamenev, D.I., Berman, G.P., Tsifrinovich, V.I.: Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction. Phys. Rev. A 74, 042337 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Zurek, W.H.: Einselection and decoherence from an information theory perspective. Annalen der Physik 9, 855 (2000)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    Bera, A., Das, T., Sadhukhan, D., Singha Roy, S., Sen, De A., Sen, U.: Quantum Discord and Its Allies: A Review. arXiv:1703.10542v1
  21. 21.
    Nielsen, M.A.: Quantum information theory. Ph.D. thesis, University of Mexico, arXiv:quant-ph/0011036 (1998)
  22. 22.
    Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. arXiv:quant-ph/0009060 (2000)
  23. 23.
    Maziero, J., Guzman, H.C., Cleri, L.C., Sarandy, M.S., Serra, R.M.: Quantum and classical thermal correlations in the XY spin-\(\frac{1}{2}\) chain. Phy. Rev. A. 82, 012106 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 30, 598 (2009)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Sharma, K.K., Awasthi, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit–qutrit systems under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 12, 3437 (2013)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Sharma, K.K., Pandey, S.N.: Entanglement dynamics in two parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 13, 2017 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Sharma, K.K., Pandey, S.N.: Influence of Dzyaloshinshkii–Moriya interaction on quantum correlations in two qubit Werner states and MEMS. Quantum Inf. Process. 14, 1361 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Sharma, K.K., Pandey, S.N.: Dzyaloshinshkii–Moriya interaction as an agent to free the bound entangled states. Quantum Inf. Process. 15, 1539 (2016)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Sharma, K.K., Pandey, S.N.: Dynamics of entanglement in two parameter qubit–qutrit states with x-component of DM interaction. Commun. Theor. Phys. 65, 278 (2016)ADSCrossRefGoogle Scholar
  31. 31.
    Sharma, K.K., Pandey, S.N.: Robustness of W and Greenberger Horne Zeilinger states against Dzyaloshinskii–Moriya interaction Quant. Inf. Proc. 15, 4995 (2016)CrossRefGoogle Scholar
  32. 32.
    Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    Cavalcanti, D., Skrzypczyk, P.: Quantum steering: a review with focus on semidefinite programming. Rep. Prog. Phys. 80, 024001 (2017)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Sainz, A.B., Aolita, L., Piani, M., Hoban, M.J., Skrzypczyk, P.: A formalism for steering with local quantum measurements, arXiv:1708.00756 (2017)
  35. 35.
    Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quant. Inf. Comp. 7, 1 (2007)MathSciNetzbMATHGoogle Scholar
  37. 37.
    Wang, C.Z., Li, C.X., Nie, L.Y., Li, J.F.: Classical correlation and quantum discord mediated by cavity in two coupled qubits. J. Phys. B At. Mol. Opt. 44, 015503 (2011)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology BombayMumbaiIndia

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