Evolution of holographic entropy quantities for composite quantum systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 510-517
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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, total correlation, secrecy monotone.
Mots-clés : tripartite information
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I. Ya. Aref'eva; I. V. Volovich; O. V. Inozemtsev. Evolution of holographic entropy quantities for composite quantum systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 510-517. http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a11/

[1] I. Ya. Arefeva, I. V. Volovich, O. V. Inozemtsev, “Golograficheskii kontrol informatsii i dinamicheskoe izmenenie topologii sostavnykh otkrytykh kvantovykh sistem”, TMF, 193:3 (2017), 493–504 | DOI | DOI | MR

[2] M. Ohya, I. Volovich, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems, Springer, Dordrecht, 2011 | DOI | MR

[3] A. S. Trushechkin, I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks”, Europhys. Lett., 113:3 (2016), 30005, 6 pp. | DOI

[4] S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, I. V. Volovich, “Flows in non-equilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021, 19 pp., arXiv: 1612.00213 | DOI | MR

[5] I. V. Volovich, S. V. Kozyrev, “Manipulyatsiya sostoyaniyami vyrozhdennoi kvantovoi sistemy”, Tr. MIAN, 294 (2016), 256–267 | DOI | DOI | MR

[6] I. V. Volovich, “Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light”, Phys. Lett. A, 380:1 (2016), 56–58 | DOI | MR

[7] I. Aref'eva, I. Volovich, Holographic photosynthesis, arXiv: 1603.09107

[8] I. Ya. Arefeva, “Golograficheskoe opisanie kvark-glyuonnoi plazmy, obrazuyuscheisya pri stolknoveniyakh tyazhelykh ionov”, UFN, 184:6 (2014), 569–598 | DOI | DOI

[9] I. Ya. Aref'eva, I. V. Volovich, “Holographic photosynthesis and entanglement entropy”, International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics, QP38 (Tokyo University of Science, Japan, 1–7 October, 2017), 2019 (to appear)

[10] S. Ryu, T. Takayanagi, “Aspects of holographic entanglement entropy”, JHEP, 08 (2006), 045, 47 pp., arXiv: hep-th/0605073 | DOI

[11] V. E. Hubeny, M. Rangamani, T. Takayanagi, “A covariant holographic entanglement entropy proposal”, JHEP, 07 (2007), 062, 64 pp., arXiv: 0705.0016 | DOI | MR

[12] D. S. Ageev, I. Ya. Arefeva, “Probuzhdenie i skrembling v protsesse golograficheskogo nagreva”, TMF, 193:1 (2017), 146–161, arXiv: 1701.07280 | DOI | DOI | MR

[13] D. S. Ageev, I. Y. Aref'eva, “Holographic non-equilibrium heating”, JHEP, 2018 (2018), 103, 18 pp., arXiv: 1704.07747 | DOI

[14] B. Groisman, S. Popescu, A. Winter, “Quantum, classical, and total amount of correlations in a quantum state”, Phys. Rev. A, 72:3 (2005), 032317, 11 pp., arXiv: quant-ph/0410091 | DOI | MR

[15] D. Ryuel, Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 171 | MR

[16] H. Araki, E. H. Lieb, “Entropy inequalities”, Commun. Math. Phys., 18:2 (1970), 160–170 | DOI

[17] H. Casini, M. Huerta, “Remarks on the entanglement entropy for disconnected regions”, JHEP, 03 (2009), 048, 19 pp., arXiv: 0812.1773 | DOI | MR

[18] P. Hayden, M. Headrick, A. Maloney, “Holographic mutual information is monogamous”, Phys. Rev. D, 87:4 (2013), 046003, 11 pp., arXiv: 1107.2940 | DOI

[19] A. Kumar, “Multiparty quantum mutual information: an alternative definition”, Phys. Rev. A, 96:1 (2017), 012332, 5 pp., arXiv: 1504.07176 | DOI

[20] S. Watanabe, “Information theoretical analysis of multivariate correlation”, IBM J. Res. Develop., 4:1 (1960), 66–82 | DOI | MR

[21] R. Horodecki, “Informationally coherent quantum systems”, Phys. Lett. A, 187:2 (1994), 145–150 | DOI | MR

[22] D. Yang, K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim, W. Song, “Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof ”, IEEE Trans. Inform. Theory, 55:7 (2009), 3375–3387, arXiv: 0704.2236 | DOI | MR

[23] M. E. Shirokov, “Mery korrelyatsii v beskonechnomernykh kvantovykh sistemakh”, Matem. sb., 207:5 (2016), 93–142 | DOI | DOI | MR | Zbl

[24] N. J. Cerf, S. Massar, S. Schneider, “Multipartite classical and quantum secrecy monotones”, Phys. Rev. A, 66:4 (2002), 042309, 13 pp., arXiv: quant-ph/0202103 | DOI

[25] S. Sazim, P. Agrawal, Quantum mutual information and quantumness vectors for multi-qubit systems, arXiv: 1607.05155

[26] K. Bradler, M. M. Wilde, S. Vinjanampathy, D. B. Uskov, “Identifying the quantum correlations in light-harvesting complexes”, Phys. Rev. A, 82:6 (2010), 062310, 12 pp., arXiv: 0912.5112 | DOI