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Temperature-field phase diagrams of one-way quantum work deficit in two-qubit XXZ spin systems

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Abstract

The spin-1/2 XXZ chain in a uniform magnetic field at thermal equilibrium is considered. For this model, we give a complete classification of all qualitatively different phase diagrams for the one-way quantum work (information) deficit. The diagrams can contain regions (phases, fractions) with both stationary and variable (state-dependent) angles of optimal measurement. We found cases of phase diagrams in which the sizes of regions with the variable optimal measurement angle are large and perhaps such regions can be detected experimentally. We also established a relationship between the behavior of optimal measurement angles near the boundaries separated different regions and Landau’s theory of phase transitions of the second and first kind.

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References

  1. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  2. Streltsov, A.: Quantum Correlations Beyond Entanglement and Their Role in Quantum information Theory. Springer, Berlin (2015)

    MATH  Google Scholar 

  3. Adesso, G., Bromley, T.R., Cianciaruso, M.: Measures and applications of quantum correlations. J. Phys. A: Math. Theor. 49, 473001 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  4. Fanchini, F.F., Soares-Pinto, D.O., Adesso, G. (eds.): Lectures on General Quantum Correlations and Their Applications. Springer, Berlin (2017)

    MATH  Google Scholar 

  5. Bera, A., Das, T., Sadhukhan, D., Roy, S.S., Sen(De), A., Sen, U.: Quantum discord and its allies: a review of recent progress. Rep. Prog. Phys. 81, 024001 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  6. Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics, vol. 1. Addison-Wesley, Reading (1964, second printing) (1964)

  7. Heisenberg, W.: Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zs. Phys. 33, 879 (1925)

    Article  ADS  Google Scholar 

  8. Wolff, J.: Heisenberg’s observability principle. In: Studies in history and philosophy of science. Part B. Stud. Hist. Philos. Mod. Phys. 45, 19 (2014)

    Article  Google Scholar 

  9. Zurek, W.H.: Einselection and decoherence from an information theory perspective. Ann. Phys. (Leipz.) 9, 855 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  10. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  12. Vedral, V.: Foundations of quantum discord. In: Fanchini, F.F., Soares-Pinto, D.O., Adesso, G. (eds.) Lectures on General Quantum Correlations and Their Applications. Springer, Berlin (2017)

    Google Scholar 

  13. Lindblad, G.: Entropy, information and quantum measurements. Commun. Math. Phys. 33, 305 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  14. Oppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002)

    Article  ADS  Google Scholar 

  15. Horodecki, M., Horodecki, K., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U.: Local information as a resource in distributed quantum systems. Phys. Rev. Lett. 90, 100402 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  16. Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 062307 (2005)

    Article  ADS  Google Scholar 

  17. Ye, B.-L., Fei, S.-M.: A note on one-way quantum deficit and quantum discord. Quantum Inf. Process. 15, 279 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  18. Feynman, R.: The Character of Physical Law. MIT, Cambridge (1985, twelfth printing). Sect. 7 Seeking new laws, p. 164 (1985)

  19. Lu, X.-M., Xi, Z., Sun, Z., Wang, X.: Geometric mesure of quantum discord under decoherence. Quantum Inf. Comput. 10, 0994 (2010)

    MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Vinjanampathy, S., Rau, A.R.P.: Quantum discord for qubit-qudit systems. J. Phys. A: Math. Theor. 45, 095303 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  22. Ye, B.-L., Wang, Y.-K., Fei, S.-M.: One-way quantum deficit and decoherence for two-qubit \(X\) states. Int. J. Theor. Phys. 55, 2237 (2016)

    Article  Google Scholar 

  23. Yurischev, M.A.: Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states. Quantum Inf. Process. 17, 6 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  24. Yurischev, M.A.: Phase diagram for the one-way quantum deficit of two-qubit X states. Quantum Inf. Process. 18, 124 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  25. Lu, X.-M., Ma, J., Xi, Z., Wang, X.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A 83, 012327 (2011)

    Article  ADS  Google Scholar 

  26. Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit \(X\) states. Phys. Rev. A 84, 042313 (2011)

    Article  ADS  Google Scholar 

  27. Huang, Y.: Quantum discord for two-qubit \(X\) states: analytical formula with very small worst-case error. Phys. Rev. A 88, 014302 (2013)

    Article  ADS  Google Scholar 

  28. Yurischev, M.A.:, Quantum discord for general X and CS states: a piecewise-analytical-numerical formula. arXiv:1404.5735v1 [quant-ph]

  29. Yurishchev, M.A.: NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore. J. Exp. Theor. Phys. 119, 828 (2014)

    Article  ADS  Google Scholar 

  30. Yurischev, M.A.: On the quantum discord of general \(X\) states. Quantum Inf. Process. 14, 3399 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  31. Yurischev, M.A.: Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states. Quantum Inf. Process. 16, 249 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  32. Canosa, N., Ciliberti, L., Rossignoli, R.: Quantum discord and information deficit in spin chains. Entropy 17, 1634 (2015). (Special issue: Quantum computation and information: Multi-particle aspects)

    Article  ADS  MathSciNet  Google Scholar 

  33. Klein, O.: Zur quantenmechanischen Begründung des zweiten Hauptsatzes der Wärmelehre. Zs. Phys. 72, 767 (1931)

    Article  ADS  Google Scholar 

  34. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, 10 anniversary edn. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  35. Fain, V.M.: Quantum Radiophysics. Photons and Nonlinear Media, vol. 1, 2nd edn. Sovetskoe Radio, Moscow (1972). [in Russian]

    Google Scholar 

  36. Dirac, P.A.M.: The Principles of Quantum Mechanics, 4th edn. Clarendon, Oxford (1958)

    MATH  Google Scholar 

  37. James, D.F.V., Kwiat, P.G., Munro, W.J., White, A.G.: Measurement of qubits. Phys. Rev. A 64, 052312 (2001)

    Article  ADS  Google Scholar 

  38. Yurischev, M.A.: Jumps of optimal measurement angle and fractures on the curves of quantum correlation functions. Proc. SPIE 11022, 1102221 (2019)

    Google Scholar 

  39. Moreva, E.V., Gramegna, M., Yurischev, M.A.: On the possibility to detect quantum correlation regions with the variable optimal measurement angle. Eur. Phys. J. D 73, 68 (2019). topical issue “Quantum correlations”

    Article  ADS  Google Scholar 

  40. Landau, L.D., Lifshitz, E.M.: Statistical Physics. Part 1. Fizmatlit, Moscow (2005) [in Russian], Pergamon, Oxford (1980) [in English]

  41. Arnold, V.I.: Catastrophe Theory. Springer, Berlin (1992)

    Book  Google Scholar 

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Acknowledgements

I am grateful to A. I. Zenchuk for his help. This work was performed as a part of the state task, State Registration No. 0089-2019-0002.

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

    M. A. Yurischev

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  1. M. A. Yurischev
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Correspondence to M. A. Yurischev.

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Yurischev, M.A. Temperature-field phase diagrams of one-way quantum work deficit in two-qubit XXZ spin systems. Quantum Inf Process 19, 110 (2020). https://doi.org/10.1007/s11128-020-2610-1

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