Geodesic
The dynamics of quantum correlations of two qubits in a common environment
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 3, pp. 228-262 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a model of quantum system of two qubits embedded into a common environment assuming that the environment parts of the system Hamiltonian are described by hermitian random matrices of size $N$. We obtain the infinite $N$ limit of the time dependent reduced density matrix of qubits. We then work out an analog of the Bogolyubov-van Hove asymptotic regime of the theory of open systems and statistical mechanics. The regime does not imply in general the Markovian dynamics of the reduced density matrix of our model and allows for a analytical and numerical analysis of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a variety of new patterns of qubits dynamics absent in the case of independent random matrix environments studied in our paper [8]. The patterns demonstrate the important role of common environment in the enhancement and the diversification of quantum correlations via the indirect (via environment) interaction between qubits. Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution that have been found in various exact and approximate versions of the two qubit models with macroscopic bosonic environment. 
@article{JMAG_2020_16_3_a2,
     author = {Ekaterina Bratus and Leonid Pastur},
     title = {The dynamics of quantum correlations of two qubits in a common environment},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {228--262},
     year = {2020},
     volume = {16},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2020_16_3_a2/}
}
TY  - JOUR
AU  - Ekaterina Bratus
AU  - Leonid Pastur
TI  - The dynamics of quantum correlations of two qubits in a common environment
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2020
SP  - 228
EP  - 262
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2020_16_3_a2/
LA  - en
ID  - JMAG_2020_16_3_a2
ER  - 
%0 Journal Article
%A Ekaterina Bratus
%A Leonid Pastur
%T The dynamics of quantum correlations of two qubits in a common environment
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2020
%P 228-262
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2020_16_3_a2/
%G en
%F JMAG_2020_16_3_a2
Ekaterina Bratus; Leonid Pastur. The dynamics of quantum correlations of two qubits in a common environment. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 3, pp. 228-262. http://geodesic.mathdoc.fr/item/JMAG_2020_16_3_a2/

[1] G. Adesso, T.R. Bromley, M. Cianciaruso, “Measures and applications of quantum correlations”, J. Phys. A: Math. Theor., 49 (2016), 473001 | DOI | MR | Zbl

[2] C. Addis, P. Haikka, S. McEndoo, C. Macchiavello, S. Maniscalco, “Two-qubit non-Markovianity induced by a common environment”, Phys. Rev. A, 87 (2013), 052109 | DOI

[3] G. Akemann, J. Baik, P. Di Francesco, The Oxford Handbook of Random Matrix Theory, Oxford University Press, 2011 | MR | Zbl

[4] L. Aolita, F. de Melo, L. Davidovich, “Open-system dynamics of entanglement”, Rep. Prog. Phys., 78 (2015), 042001 | DOI

[5] A. Bera, T. Das, D. Sadhukhan, S.S. Roy, A. Sen(De), U. Sen, “Quantum discord and its allies: a review of recent progress”, Rep. Prog. Phys., 81 (2017), 024001 | DOI | MR

[6] N.N. Bogolyubov, On Some Statistical Methods in Mathematical Physics, Izd. AN USSR, Kiev, 1945 (Russian) | MR

[7] N.N. Bogoliubov, Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York, 1962 | MR

[8] E. Bratus, L. Pastur, “On the qubit dynamics in random matrix environment”, J. Phys. Commun., 2 (2018), 015017 | DOI

[9] E. Bratus, L. Pastur, “Dynamics of two qubits in common environment”, Rev. Math. Phys., 32 (2020), 2060008 | MR

[10] H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, Oxford, 2007 | MR | Zbl

[11] H.-P. Breuer, E.-M. Laine, J. Piilo, B. Vacchini, “Non-Markovian dynamics in open quantum systems”, Rev. Mod. Phys., 88 (2016), 021002 | DOI

[12] J. Dajka, M. Mierzejewski, J. Luczka, R. Blattmann, P. Hänggi, “Negativity and quantum discord in Davies environments”, J. Phys. A: Math.Theor., 45 (2012), 485306 | DOI | MR | Zbl

[13] O.C.O. Dahlsten, C. Lupo, S. Mancini, A. Serafini, “Entanglement typicality”, J. Phys. A: Math. Theor., 47 (2014), 363001 | DOI | MR | Zbl

[14] E.B. Davies, Quantum Theory of Open System, Academic Press, New York, 1976 | MR

[15] I. de Vega and D. Alonso, “Dynamics of non-Markovian open quantum systems”, Rev. Mod. Phys., 89 (2017), 015001 | DOI | MR

[16] T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, W. Zwerger, Quantum Transport and Dissipation, Willey-VCH, Weinheim, 1998 | Zbl

[17] C. Eltschka, J. Siewert, “Quantifying entanglement resources”, J. Phys. A: Math. Theor., 47 (2014), 424005 | DOI | MR | Zbl

[18] P.J. Forrester, Log-Gases and Random Matrices, Princeton University Press, Princeton, 2010 | MR | Zbl

[19] T. Guhr, A. Mueller-Groeling, H.A. Weidenmueller, “Random-matrix theories in quantum physics: common concepts”, Phys. Rep., 299 (1998), 189–495 | DOI | MR

[20] R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, “Quantum entanglement”, Rev. Mod. Phys., 81 (2009), 865–942 | DOI | MR | Zbl

[21] L. Landau, E. Lifshitz, Statistical Physics, Elsevier Science, Amsterdam, 1980

[22] J.L. Lebowitz, L. Pastur, “A random matrix model of relaxation”, J. Phys. A: Math. Gen., 37 (2004), 1517–1534 | DOI | MR | Zbl

[23] I.M. Lifshitz, S.A. Gredeskul, L. A. Pastur, Introduction to the Theory of Disordered Systems, Wiley, New York, 1988 | MR

[24] R. Lo Franco, B. Bellomo, S. Maniscalco, G. Compagno, “Dynamics of quantum correlations in two-qubit system within non-Markovian environment”, Int. J. Mod. Phys. B, 27 (2013), 1345053 | DOI | MR | Zbl

[25] L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs”, Phys. Rev. A, 79 (2009), 042302 | DOI

[26] L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, “Exact dynamics of entanglement and entropy in structured environments”, J. Phys. B: At. Mol. Opt. Phys., 43 (2010), 085505 | DOI

[27] S. Milz, M.S. Kim, F.A. Pollock, K. Modi, “Completely positive divisibility does not mean Markovianity”, Phys. Rev. Let., 123 (2019), 040401 | DOI | MR

[28] S.A. Molchanov, L.A. Pastur, A.M. Khorunzhii, “Limiting eigenvalue distribution for band random matrices”, Teor. Math. Phys., 90 (1992), 108–118 | DOI | MR | Zbl

[29] N.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000 | MR | Zbl

[30] M. Ohya, I. Volovich, Mathematical Foundations of Quantum Informationand Computation and Its Applications to Nano- and Bio-Systems, Springer, New York, 2011 | MR

[31] L. Pastur, M. Shcherbina, Eigenvalue Distribution of Large Random Matrices, American Mathematical Society, Providence, RI, 2011 | MR | Zbl

[32] A. Rivas, S. F. Huelga, M. B. Plenio, “Quantum non-Markovianity: characterization, quantification and detection”, Rep. Prog. Phys., 77 (2014), 094001 | DOI | MR

[33] H. Spohn, “Kinetic equations from Hamiltonian dynamics: Markovian limits”, Rev. Mod. Phys., 52 (1980), 569–615 | DOI | MR

[34] L. van Hove, “The approach to equilibrium in quantum statistics: A perturbation treatment to general order”, Physica, 23 (1955), 441–480 | MR

[35] N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier Science, Amsterdam, 2011 | MR

[36] W.K. Wooters, “Entanglement of formation and concurrence”, Quantum Inf. Comput., 1 (2001), 27–44 | MR

[37] T. Yu, J.H. Eberly, “Finite-time disentanglement via spontaneous emission”, Phys. Rev. Lett., 93 (2004), 140404 | DOI

[38] T. Yu, J.H. Eberly, “Sudden death of entanglement”, Science, 323 (2009), 598–601 | DOI | MR | Zbl

[39] T. Yu, J.H. Eberly, “Entanglement evolution in a non-Markovian environment”, Opt. Commun., 283 (2010), 676–680 | DOI

[40] K. Zyczkowski, P. Horodecki, M. Horodecki, R. Horodecki, “Dynamics of quantum entanglement”, Phys. Rev. A, 65 (2001), 012101 | DOI | MR