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Probing quantum coherence, uncertainty, steerability of quantum coherence and quantum phase transition in the spin model

Article

Abstract

In this paper, we study the relation among quantum coherence, uncertainty, steerability of quantum coherence based on skew information and quantum phase transition in the spin model by employing quantum renormalization-group method. Interestingly, the results show that the value of the local quantum uncertainty is equal to the local quantum coherence corresponding to local observable \(\sigma _z\) in XXZ model, and unlikely in XY model, local quantum uncertainty is minimal optimization of the local quantum coherence over local observable \(\sigma _x\) and this proposition can be generalized to a multipartite system. Therefore, one can directly achieve quantum correlation measured by local quantum uncertainty and coherence by choosing different local observables \(\sigma _x\), \(\sigma _z\), corresponding to the XY model and XXZ model separately. Meanwhile, steerability of quantum coherence in XY and XXZ model is investigated systematically, and our results reveal that no matter what times the QRG iterations are carried out, the quantum coherence of the state of subsystem cannot be steerable, which can also be suitable for block–block steerability of local quantum coherence in both XY and XXZ models. On the other hand, we have illustrated that the quantum coherence and uncertainty measure can efficiently detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization. Moreover, the nonanalytic and scaling behaviors of steerability of local quantum coherence have been also taken into consideration.

Keywords

Quantum uncertainty Quantum coherence Quantum phase transition Spin model 

Notes

Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 11575001 and 11605028, and also by the Natural Science Research Project of Education Department of Anhui Province of China (Grant No. KJ2013A205).

References

  1. 1.
    Glauber, R.J.: The quantum theory of optical coherence. Phys. Rev. 130(6), 2529 (1963)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University, Cambridge (2000)MATHGoogle Scholar
  3. 3.
    Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008)ADSMathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Olliver, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSMATHCrossRefGoogle Scholar
  6. 6.
    Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)ADSMathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Vedral, V.: Classical correlations and entanglement in quantum measurements. Phys. Rev. Lett. 90, 050401 (2003)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113(14), 140401 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    Aberg, J.: Quantifying Superposition. arXiv:quant-ph/0612146
  10. 10.
    Shao, L.-H., Xi, Z., Fan, H., Li, Y.: Fidelity and trace-norm distances for quantifying coherence. Phys. Rev. A. 91, 042120 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    Streltsov, A.: Genuine Quantum Coherence. arXiv:1511.08346
  12. 12.
    Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Xi, Z., Li, Y., Fan, H.: Quantum coherence and correlations in quantum system. Sci. Rep. 5, 10922 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Liu, C.C., Shi, J.D., Ding, Z.Y., Ye, L.: Exploring the renormalization of quantum discord and Bell non-locality in the one-dimensional transverse Ising model. Quantum Inf. Process. 15, 3209–3221 (2016)ADSMathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSMATHCrossRefGoogle Scholar
  17. 17.
    Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. 105, 095702 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    Osterloh, A., Plastina, F., Fazio, R., Palma, G.M.: Dynamics of entanglement in one-dimensional spin systems. Phys. Rev. A 69, 022304 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, Cambridge (2011)MATHCrossRefGoogle Scholar
  21. 21.
    Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)ADSCrossRefGoogle Scholar
  22. 22.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008)ADSMathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110(24), 240402 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    Wigner, E.P., Yanase, M.M.: Information content of distribution. Proc. Natl. Acad. Sci. USA 49, 910–918 (1963)ADSMathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Vidal, G.: Entanglement renormalization. Phys. Rev. Lett. 99, 220405 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    Ferrenberg, A.M., Swendsen, R.H.: New Monte Carlo technique for studying phase transitions. Phys. Rev. Lett. 61, 2635 (1988)ADSCrossRefGoogle Scholar
  27. 27.
    Wolf, M.M., Ortiz, G., Verstraete, F., Cirac, J.I.: Quantum phase transitions in matrix product systems. Phys. Rev. Lett. 97, 110403 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    Wilson, K.G.: The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773 (1975)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Pefeuty, P., Jullian, R., Penson, K.L.: In: Burkhardt, T.W., van Leeuwen J.M.J. (eds.) Real-Space Renormalizaton, Chap. 5. Springer, Berlin (1982)Google Scholar
  30. 30.
    Langari, A.: Quantum renormalization group of XYZ model in a transverse magnetic field. Phys. Rev. B 69, 100402(R) (2004)ADSCrossRefGoogle Scholar
  31. 31.
    Mondal, D., Pramanik, T., Pati, A.K.: Steerability of Local Quantum Coherence. arXiv:1508.03770v2 (2015)
  32. 32.
    Gupta, R., DeLapp, J., Batrouni, G.G., Fox, G.C., Baille, C.F., Apostolakis, J.: Phase Transition in the 2D XY model. Phys. Rev. Lett. 61, 1996 (1988)ADSCrossRefGoogle Scholar
  33. 33.
    Karpat, G., Cakmak, B., Fanchini, F.F.: Quantum coherence and uncertainty in the anisotropic XY chain. Phys. Rev. B 90(10), 104431 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum metrology. Phys. Rev. Lett. 96(1), 010401 (2006)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Rau, A.R.P.: Algebraic characterization of X-states in quantum information. J. Phys. A 42, 412002 (2009)MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    Latorre, J.I., Lütken, C.A., Rico, E., Vidal, G.: Fine-grained entanglement loss along renormalization-group flows. Phys. Rev. A 71, 034301 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Physics and Material ScienceAnhui UniversityHefeiChina

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