Pure non-Markovian evolutions

Dario De Santis

ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
Scuola Normale Superiore, I-56126 Pisa, Italy

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Non-Markovian dynamics are characterized by information backflows, where the evolving open quantum system retrieves part of the information previously lost in the environment. Hence, the very definition of non-Markovianity implies an initial time interval when the evolution is noisy, otherwise no backflow could take place. We identify two types of initial noise, where the first has the only effect of degrading the information content of the system, while the latter is essential for the appearance of non-Markovian phenomena. Therefore, all non-Markovian evolutions can be divided into two classes: noisy non-Markovian (NNM), showing both types of noise, and pure non-Markovian (PNM), implementing solely essential noise. We make this distinction through a timing analysis of fundamental non-Markovian features. First, we prove that all NNM dynamics can be simulated through a Markovian pre-processing of a PNM core. We quantify the gains in terms of information backflows and non-Markovianity measures provided by PNM evolutions. Similarly, we study how the entanglement breaking property behaves in this framework and we discuss a technique to activate correlation backflows. Finally, we show the applicability of our results through the study of several well-know dynamical models.

► BibTeX data

► References

[1] H.-P. Breuer and F. Petruccione. ``The Theory of Open Quantum Systems''. Oxford University Press. (2007).

[2] Á. Rivas and S. F. Huelga. ``Open quantum systems. an introduction''. Springer, Heidelberg. (2011).

[3] D. Chruściński. ``Dynamical maps beyond markovian regime''. Physics Reports 992, 1–85 (2022).

[4] Á. Rivas, S. F. Huelga, and M. B. Plenio. ``Quantum non-markovianity: characterization, quantification and detection''. Reports on Progress in Physics 77, 094001 (2014).

[5] H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini. ``Colloquium: Non-markovian dynamics in open quantum systems''. Rev. Mod. Phys. 88, 021002 (2016).

[6] I. de Vega and D. Alonso. ``Dynamics of non-markovian open quantum systems''. Rev. Mod. Phys. 89, 015001 (2017).

[7] Li L., M. J. W. Hall, and H. M. Wiseman. ``Concepts of quantum non-markovianity: A hierarchy''. Physics Reports 759, 1–51 (2018).

[8] D. Chruściński, Á. Rivas, and E. Størmer. ``Divisibility and information flow notions of quantum markovianity for noninvertible dynamical maps''. Phys. Rev. Lett. 121, 080407 (2018).

[9] W. F. Stinespring. ``Positive functions on c*-algebras''. Proceedings of the American Mathematical Society 6, 211–216 (1955).

[10] K. Kraus. ``General state changes in quantum theory''. Annals of Physics 64, 311–335 (1971).

[11] B. Bylicka, M. Johansson, and A. Acín. ``Constructive method for detecting the information backflow of non-markovian dynamics''. Phys. Rev. Lett. 118, 120501 (2017).

[12] D. De Santis, M. Johansson, B. Bylicka, N. K. Bernardes, and A. Acín. ``Correlation measure detecting almost all non-markovian evolutions''. Phys. Rev. A 99, 012303 (2019).

[13] F. Buscemi and N. Datta. ``Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes''. Phys. Rev. A 93, 012101 (2016).

[14] D. De Santis and M. Johansson. ``Equivalence between non-markovian dynamics and correlation backflows''. New Journal of Physics 22, 093034 (2020).

[15] M.-D. Choi. ``Completely positive linear maps on complex matrices''. Linear Algebra and its Applications 10, 285–290 (1975).

[16] A. Jamiołkowski. ``Linear transformations which preserve trace and positive semidefiniteness of operators''. Reports on Mathematical Physics 3, 275–278 (1972).

[17] Á. Rivas, S. F. Huelga, and M. B. Plenio. ``Entanglement and non-markovianity of quantum evolutions''. Phys. Rev. Lett. 105, 050403 (2010).

[18] D. Chruściński and F. A. Wudarski. ``Non-markovian random unitary qubit dynamics''. Physics Letters A 377, 1425–1429 (2013).

[19] M. J. W. Hall, J. D. Cresser, L. Li, and E. Andersson. ``Canonical form of master equations and characterization of non-markovianity''. Phys. Rev. A 89, 042120 (2014).

[20] F. Benatti, D. Chruściński, and S. Filippov. ``Tensor power of dynamical maps and positive versus completely positive divisibility''. Phys. Rev. A 95, 012112 (2017).

[21] N. Megier, D. Chruściński, J. Piilo, and W. T. Strunz. ``Eternal non-markovianity: from random unitary to markov chain realisations''. Sci. Rep. 7, 6379 (2017).

[22] D. De Santis, M. Johansson, B. Bylicka, N. K. Bernardes, and A. Acín. ``Witnessing non-markovian dynamics through correlations''. Phys. Rev. A 102, 012214 (2020).

[23] H.-P. Breuer, E.-M. Laine, and J. Piilo. ``Measure for the degree of non-markovian behavior of quantum processes in open systems''. Phys. Rev. Lett. 103, 210401 (2009).

[24] S. Luo, S. Fu, and H. Song. ``Quantifying non-markovianity via correlations''. Phys. Rev. A 86, 044101 (2012).

[25] C. Addis, B. Bylicka, D. Chruściński, and S. Maniscalco. ``Comparative study of non-markovianity measures in exactly solvable one- and two-qubit models''. Phys. Rev. A 90, 052103 (2014).

[26] D. De Santis and V. Giovannetti. ``Measuring non-markovianity via incoherent mixing with markovian dynamics''. Phys. Rev. A 103, 012218 (2021).

[27] D. Chruściński and S. Maniscalco. ``Degree of non-markovianity of quantum evolution''. Phys. Rev. Lett. 112, 120404 (2014).

[28] C. Pineda, T. Gorin, D. Davalos, D. A. Wisniacki, and I. García-Mata. ``Measuring and using non-markovianity''. Phys. Rev. A 93, 022117 (2016).

[29] J. Kołodyński, S. Rana, and A. Streltsov. ``Entanglement negativity as a universal non-markovianity witness''. Phys. Rev. A 101, 020303 (2020).

[30] D. De Santis, D. Farina, M. Mehboudi, and A. Acín. ``Ancillary gaussian modes activate the potential to witness non-markovianity''. New Journal of Physics 25, 023025 (2023).

[31] X.-M. Lu, X. Wang, and C. P. Sun. ``Quantum fisher information flow and non-markovian processes of open systems''. Phys. Rev. A 82, 042103 (2010).

[32] P. Abiuso, M. Scandi, D. De Santis, and J. Surace. ``Characterizing (non-)Markovianity through Fisher information''. SciPost Phys. 15, 014 (2023).

[33] S. Lorenzo, F. Plastina, and M. Paternostro. ``Geometrical characterization of non-markovianity''. Phys. Rev. A 88, 020102 (2013).

[34] M. M. Wolf and J. I. Cirac. ``Dividing quantum channels''. Commun. Math. Phys. 279, 147–168 (2008).

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2024-05-21 13:32:22). On SAO/NASA ADS no data on citing works was found (last attempt 2024-05-21 13:32:22).