Advertisement

Theoretical and Mathematical Physics

, Volume 197, Issue 3, pp 1838–1844 | Cite as

Evolution of Holographic Entropy Quantities for Composite Quantum Systems

  • I. Ya. Aref’evaEmail author
  • I. V. Volovich
  • O. V. Inozemcev
Article
  • 3 Downloads

Abstract

We consider entanglement entropy quantities for a three-part system, namely, the tripartite information, total correlation, and so-called secrecy monotone. A holographic approach is used to calculate the time evolution of the entanglement entropy during nonequilibrium heating, which leads to holographic definitions of these quantities. We study time dependence of these three quantities.

Keywords

Vaidya–AdS space tripartite information total correlation secrecy monotone 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. Ya. Aref’eva, I. V. Volovich, and O. V. Inozemcev, “Holographic control of information and dynamical topology change for composite open quantum systems,” Theor. Math. Phys., 193, 1834–1843 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    M. Ohya and I. Volovich, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems, Springer, Dordrecht (2011).CrossRefzbMATHGoogle Scholar
  3. 3.
    A. S. Trushechkin and I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks,” Europhys. Lett., 113, 30005 (2016).CrossRefGoogle Scholar
  4. 4.
    S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, and I. V. Volovich, “Flows in non-equilibrium quantum systems and quantum photosynthesis,” Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20, 1750021 (2017); arXiv:1612.00213v1 [quant-ph] (2016).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    I. V. Volovich and S. V. Kozyrev, “Manipulation of states of a degenerate quantum system,” Proc. Steklov Inst. Math., 294, 241–251 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    I. V. Volovich, “Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light,” Phys. Lett. A, 380, 56–58 (2016).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    I. Aref’eva and I. Volovich, “Holographic photosynthesis,” arXiv:1603.09107v2 [hep-th] (2016).Google Scholar
  8. 8.
    I. Ya. Aref’eva, “Holographic approach to quark–gluon plasma in heavy ion collisions,” Phys. Usp., 57, 527–555 (2014).CrossRefGoogle Scholar
  9. 9.
    I. Ya. Aref’eva and I. V. Volovich, “Holographic photosynthesis and entanglement entropy,” in: Intl. Conf. Infinite Dimensional Analysis, Quantum Probability, and Related Topics, QP38 (Tokyo University of Science, Japan, 1–7 October 2017) (to appear).Google Scholar
  10. 10.
    S. Ryu and T. Takayanagi, “Aspects of holographic entanglement entropy,” JHEP, 0608, 045 (2006); arXiv:hepth/0605073v3 (2006).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    V. E. Hubeny, M. Rangamani, and T. Takayanagi, “A covariant holographic entanglement entropy proposal,” JHEP, 0707, 062 (2007); arXiv:0705.0016v3 [hep-th] (2007).ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    D. S. Ageev and I. Ya. Aref’eva, “Waking and scrambling in holographic heating up,” Theor. Math. Phys., 193, 1534–1546 (2017); arXiv:1701.07280v2 [hep-th] (2017).CrossRefzbMATHGoogle Scholar
  13. 13.
    D. S. Ageev and I. Y. Aref’eva, “Holographic non-equilibrium heating,” JHEP, 1803, 103 (2018); arXiv: 1704.07747v3 [hep-th] (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    B. Groisman, S. Popescu, and A. Winter, “Quantum, classical, and total amount of correlations in a quantum state,” Phys. Rev. A, 72, 032317 (2005); arXiv:quant-ph/0410091v2 (2004).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, New York (1969).zbMATHGoogle Scholar
  16. 16.
    H. Araki and E. H. Lieb, “Entropy inequalities,” Commun. Math. Phys., 18, 160–170 (1970).ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    H. Casini and M. Huerta, “Remarks on the entanglement entropy for disconnected regions,” JHEP, 0903, 048 (2009); arXiv:0812.1773v2 [hep-th] (2008).ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    P. Hayden, M. Headrick, and A. Maloney, “Holographic mutual information is monogamous,” Phys. Rev. D, 87, 046003 (2013); arXiv:1107.2940v2 [hep-th] (2011).ADSCrossRefGoogle Scholar
  19. 19.
    A. Kumar, “Multiparty quantum mutual information: An alternative definition,” Phys. Rev. A, 96, 012332 (2017); arXiv:1504.07176v2 [quant-ph] (2015).ADSCrossRefGoogle Scholar
  20. 20.
    S. Watanabe, “Information theoretical analysis of multivariate correlation,” IBM J. Res. Develop., 4, 66–82 (1960).MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    R. Horodecki, “Informationally coherent quantum systems,” Phys. Lett. A, 187, 145–150 (1994).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    D. Yang, K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim, and W. Song, “Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof,” IEEE Trans. Inform. Theory, 55, 3375–3387 (2009); arXiv:0704.2236v3 [quant-ph] (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    M. E. Shirokov, “Measures of correlations in infinite-dimensional quantum systems,” Sb. Math., 207, 724–768 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    N. J. Cerf, S. Massar, and S. Schneider, “Multipartite classical and quantum secrecy monotones,” Phys. Rev. A, 66, 042309 (2002); arXiv:quant-ph/0202103v1 (2002).ADSCrossRefGoogle Scholar
  25. 25.
    S. Sazim and P. Agrawal, “Quantum mutual information and quantumness vectors for multi-qubit systems,” arXiv:1607.05155v1 [quant-ph] (2016).Google Scholar
  26. 26.
    K. Bradler, M. M. Wilde, S. Vinjanampathy, and D. B. Uskov, “Identifying the quantum correlations in lightharvesting complexes,” Phys. Rev. A, 82, 062310 (2010); arXiv:0912.5112g508v2 [quant-ph] (2009).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • I. Ya. Aref’eva
    • 1
    Email author
  • I. V. Volovich
    • 1
  • O. V. Inozemcev
    • 1
  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

Personalised recommendations