On the connection between microscopic description and memory effects in open quantum system dynamics

Andrea Smirne, Nina Megier, and Bassano Vacchini

Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milan, Italy

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


The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.

What are the key physical mechanisms behind the occurrence of memory effects in quantum dynamics? While in the last years several characterizations of non-Markovian evolutions in open quantum systems have been developed, each capturing a different facet of the memory due to the interaction with the environment, we are still lacking a full understanding of the microscopic origin of non-Markovianity.
In this paper, we address this question relying on the analysis of the information exchange between an open quantum system and its environment. We consider two microscopic models that, despite different coupling terms and initial environmental states, possess exactly the same reduced dynamics. Using the trace distance to quantify the information within the open system and at the level of the global evolution, we clarify how quantitatively and even qualitatively different behaviors of the system-environment correlations and environmental-state distinguishability can result in the same back-flow of information to the open system, thus leading to the very same memory effects in the evolution.

► BibTeX data

► References

[1] H.-P. Breuer and F. Petruccione. The Theory of Open Quantum Systems. Oxford University Press, Oxford, 2002.

[2] Á. Rivas and S.F. Huelga. Open Quantum Systems: An Introduction. Springer, 2012.

[3] W. Feller. An Introduction to Probability Theory and Its Applications. Wiley, New York, 1971.

[4] B. Vacchini, A. Smirne, E.-M. Laine, J. Piilo, and H.-P. Breuer. Markovianity and non-Markovianity in quantum and classical systems. New J. Phys., 13:093004, 2011. DOI: 10.1088/​1367-2630/​13/​9/​093004.

[5] B. Vacchini. A classical appraisal of quantum definitions of non-Markovian dynamics. J. Phys. B, 45:154007, 2012. DOI: 10.1088/​0953-4075/​45/​15/​154007.

[6] Á. Rivas, S.F. Huelga, and M.B. Plenio. Quantum non-Markovianity: characterization, quantification and detection. Rep. Progr. Phys., 77:094001, 2014. DOI: 10.1088/​0034-4885/​77/​9/​094001.

[7] 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.

[8] 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.

[9] E.-M. Laine, J. Piilo, and H.-P. Breuer. Measure for the non-Markovianity of quantum processes. Phys. Rev. A, 81:062115, 2010.

[10] C. A. Fuchs and J. van de Graaf. Cryptographic distinguishability measures for quantum-mechanical states. IEEE Transactions on Information Theory, 45:1216, 1999. DOI: 10.1109/​18.761271.

[11] L. Li, M. Hall, and H. Wiseman. Concepts of quantum non-Markovianity: A hierarchy. Phys. Rep., 759:1, 2018. DOI: 10.1016/​j.physrep.2018.07.001.

[12] I. de Vega and D. Alonso. Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys., 89:015001, 2017.

[13] C.-F. Li, G.-C. Guo, and J. Piilo. Non-Markovian quantum dynamics: What does it mean? EPL (Europhysics Letters), 127:50001, 2019. DOI: 10.1209/​0295-5075/​127/​50001.

[14] B.-H. Liu, L. Li, Y.-F. Huang, C.-F. Li, G.-C. Guo, E.-M. Laine, H.-P. Breuer, and J. Piilo. Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nat. Phys., 7:931, 2011. DOI: 10.1038/​nphys2085.

[15] N.K. Bernardes, J.P.S. Peterson, R.S. Sarthour, A.M. Souza, C. H. Monken, I. Roditi, Oliveira I.S., and M.F. Santos. High resolution non-Markovianity in NMR. Sci.Rep., 6:33945, 2016. DOI: 10.1038/​srep33945.

[16] S. Cialdi, M.A.C. Rossi, C. Benedetti, B. Vacchini, D. Tamascelli, S. Olivares, and M.G.A. Paris. All-optical quantum simulator of qubit noisy channels. Appl. Phys. Lett., 110:081107, 2017. DOI: 10.1063/​1.4977023.

[17] J. F. Haase, P. J. Vetter, T. Unden, A. Smirne, J. Rosskopf, B. Naydenov, A. Stacey, F. Jelezko, M. B. Plenio, and S. F. Huelga. Controllable non-Markovianity for a spin qubit in diamond. Phys. Rev. Lett., 121:060401, 2018.

[18] M. Wittemer, G. Clos, H.-P. Breuer, U. Warring, and T. Schaetz. Measurement of quantum memory effects and its fundamental limitations. Phys. Rev. A, 97:020102, 2018. DOI: 10.1103/​PhysRevA.97.020102.

[19] C.-F. Li, G.-C. Guo, and J. Piilo. Non-Markovian quantum dynamics: What is it good for? EPL (Europhysics Letters), 128:30001, 2020. DOI: 10.1209/​0295-5075/​128/​30001.

[20] E.-M. Laine, J. Piilo, and H.-P. Breuer. Witness for initial system-environment correlations in open-system dynamics. EPL (Europhysics Letters), 92:60010, 2010. DOI: 10.1209/​0295-5075/​92/​60010.

[21] L. Mazzola, C. A. Rodríguez-Rosario, K. Modi, and M. Paternostro. Dynamical role of system-environment correlations in non-Markovian dynamics. Phys. Rev. A, 86:010102, 2012. DOI: 10.1103/​PhysRevA.86.010102.

[22] A. Smirne, L. Mazzola, M. Paternostro, and B. Vacchini. Interaction-induced correlations and non-Markovianity of quantum dynamics. Phys. Rev. A, 87:052129, 2013. DOI: 10.1103/​PhysRevA.87.052129.

[23] S. Campbell, M. Popovic, D. Tamascelli, and B. Vacchini. Precursors of non-Markovianity. New J. Phys., 21(5):053036, 2019. DOI: 10.1088/​1367-2630/​ab1ed6.

[24] Nina Megier, Andrea Smirne, and Bassano Vacchini. Entropic bounds on information backflow. e-print arXiv:2101.02720, 2021.

[25] I. Bengtsson and K. Zyczkowski. Geometry of quantum states: an introduction to quantum entanglement. Cambridge University Press, Cambridge, 2006.

[26] H. Ollivier and W. H. Zurek. Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett., 88:017901, 2001. DOI: 10.1103/​PhysRevLett.88.017901.

[27] L. Henderson and V. Vedral. Classical, quantum and total correlations. Journal of Physics A: Mathematical and General, 34:6899, 2001. DOI: 10.1088/​0305-4470/​34/​35/​315.

[28] K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral. The classical-quantum boundary for correlations: Discord and related measures. Rev. Mod. Phys., 84:1655, 2012. DOI: 10.1103/​RevModPhys.84.1655.

[29] A. Pernice and W. T. Strunz. Decoherence and the nature of system-environment correlations. Phys. Rev. A, 84:062121, 2011. DOI: 10.1103/​PhysRevA.84.062121.

[30] A. Pernice, J. Helm, and W. T. Strunz. System–environment correlations and non-Markovian dynamics. J. Phys. B: Atomic, Molecular and Optical Physics, 45:154005, 2012. DOI: 10.1088/​0953-4075/​45/​15/​154005.

[31] 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. DOI: 10.1103/​ PhysRevA.99.012303.

[32] J. Kołodyński, S. Rana, and A. Streltsov. Entanglement negativity as a universal non-Markovianity witness. Phys. Rev. A, 101:020303, 2020. DOI: 10.1103/​ PhysRevA.101.020303.

[33] D. De Santis and M. Johansson. Equivalence between non-Markovian dynamics and correlation backflows. New J. Physics, 22:093034, 2020. DOI: 10.1088/​1367-2630/​abaf6a.

[34] 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. DOI: 10.1103/​PhysRevA.102.012214.

[35] F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim, M. Paternostro, and K. Modi. Operational Markov condition for quantum processes. Phys. Rev. Lett., 120:040405, 2018. DOI: 10.1103/​PhysRevLett.120.040405.

[36] S. Milz, M. S. Kim, F. A. Pollock, and K. Modi. Completely positive divisibility does not mean Markovianity. Phys. Rev. Lett., 123:040401, 2019. DOI: 10.1103/​PhysRevLett.123.040401.

[37] A. Smirne, D. Egloff, M. G. Díaz, M. B. Plenio, and S. F. Huelga. Coherence and non-classicality of quantum Markov processes. Quantum Sci. Technol., 4:01LT01, 2019. DOI: 10.1088/​2058-9565/​aaebd5.

[38] S. Milz, F. Sakuldee, F. A. Pollock, and K. Modi. Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories. Quantum, 4:255, 2020. DOI: 10.22331/​q-2020-04-20-255.

[39] S. Milz, D. Egloff, P. Taranto, T. Theurer, M. B. Plenio, A. Smirne, and S. F. Huelga. When is a non-Markovian quantum process classical? Phys. Rev. X, 10:041049, 2020. DOI: 10.1103/​PhysRevX.10.041049.

[40] M. M. Wolf, J. Eisert, T. S. Cubitt, and J. I. Cirac. Assessing non-Markovian quantum dynamics. Phys. Rev. Lett., 101:150402, 2008. DOI: 10.1103/​PhysRevLett.101.150402.

[41] Á. Rivas, S. F. Huelga, and M. B. Plenio. Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett., 105:050403, 2010. DOI: 10.1103/​PhysRevLett.105.050403.

[42] 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. DOI: 10.1103/​PhysRevA.82.042103.

[43] D. Chruściński and S. Maniscalco. Degree of non-Markovianity of quantum evolution. Phys. Rev. Lett., 112:120404, 2014. DOI: 10.1103/​PhysRevLett.112.120404.

[44] 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. DOI: 10.1103/​PhysRevA.89.042120.

[45] 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. DOI: 10.1103/​PhysRevA.93.012101.

[46] N. Megier, D. Chruściński, J. Piilo, and W. T. Strunz. Eternal non-Markovianity: from random unitary to Markov chain realisations. Sci. Rep., 7:16379, 2017. DOI: 10.1038/​s41598-017-06059-5.

[47] H. R. Jahromi, K. Mahdavipour, M. Khazaei Shadfar, and R. Lo Franco. Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed. Phys. Rev. A, 102:022221, 2020. DOI: 10.1103/​PhysRevA.102.022221.

[48] D. Chruściński, A. Kossakowski, and Á. Rivas. Measures of non-Markovianity: Divisibility versus backflow of information. Phys. Rev. A, 83:052128, 2011. DOI: 10.1103/​PhysRevA.83.052128.

[49] S. Wißmann, H.-P. Breuer, and B. Vacchini. Generalized trace-distance measure connecting quantum and classical non-Markovianity. Phys. Rev. A, 92:042108, 2015. DOI: 10.1103/​PhysRevA.92.042108.

[50] A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín. Almost all quantum states have nonclassical correlations. Phys. Rev. A, 81:052318, May 2010. DOI: 10.1103/​PhysRevA.81.052318.

[51] D. Tamascelli, A. Smirne, S. F. Huelga, and M. B. Plenio. Nonperturbative treatment of non-Markovian dynamics of open quantum systems. Phys. Rev. Lett., 120:030402, 2018. DOI: 10.1103/​PhysRevLett.120.030402.

[52] D. Tamascelli, A. Smirne, J. Lim, S. F. Huelga, and M. B. Plenio. Efficient simulation of finite-temperature open quantum systems. Phys. Rev. Lett., 123:090402, 2019. DOI: 10.1103/​PhysRevLett.123.090402.

[53] F. Chen, E. Arrigoni, and M. Galperin. Markovian treatment of non-Markovian dynamics of open Fermionic systems. New J. Phys., 21:123035, 2019. DOI: 10.1088/​1367-2630/​ab5ec5.

[54] N. Lambert, S. Ahmed, M. Cirio, and F. Nori. Modelling the ultra-strongly coupled spin-boson model with unphysical modes. Nat. Commun., 10:3721, 2019. DOI: 10.1038/​s41467-019-11656-1.

[55] A. Nüßeler, I. Dhand, S. F. Huelga, and M. B. Plenio. Efficient simulation of open quantum systems coupled to a fermionic bath. Phys. Rev. B, 101:155134, 2020. DOI: 10.1103/​PhysRevB.101.155134.

[56] G. Pleasance, B. M. Garraway, and F. Petruccione. Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes. Phys. Rev. Research, 2:043058, 2020. DOI: 10.1103PhysRevResearch.2.043058.

[57] M. G. Díaz, B. Desef, M. Rosati, D. Egloff, J. Calsamiglia, A. Smirne, M. Skotiniotis, and S. F. Huelga. Accessible coherence in open quantum system dynamics. Quantum, 4:249, 2020. DOI: 10.22331/​q-2020-04-02-249.

[58] M.A. Nielsen and I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000.

[59] A. Peres. Separability criterion for density matrices. Phys. Rev. Lett., 77:1413–1415, 1996. DOI: 10.1103/​PhysRevLett.77.1413.

[60] M. Horodecki, P. Horodecki, and R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 223:1, 1996. DOI: 10.1016/​S0375-9601(96)00706-2.

[61] K. Roszak and Ł. Cywiński. Characterization and measurement of qubit-environment-entanglement generation during pure dephasing. Phys. Rev. A, 92:032310, 2015. DOI: 10.1103/​PhysRevA.92.032310.

[62] A. C. S. Costa, M. W. Beims, and W. T. Strunz. System-environment correlations for dephasing two-qubit states coupled to thermal baths. Phys. Rev. A, 93:052316, 2016. DOI: 10.1103/​PhysRevA.93.052316.

[63] W. K. Wootters. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett., 80:2245, 1998. DOI: 10.1103/​PhysRevLett.80.2245.

[64] A. Imamoglu. Stochastic wave-function approach to non-Markovian systems. Phys. Rev. A, 50:3650, 1994. DOI: 10.1103/​PhysRevA.50.3650.

[65] B. M. Garraway. Nonperturbative decay of an atomic system in a cavity. Phys. Rev. A, 55:2290, 1997. DOI: 10.1103/​PhysRevA.55.2290.

[66] A. D. Somoza, O. Marty, J. Lim, S. F. Huelga, and M. B. Plenio. Dissipation-Assisted Matrix Product Factorization. Phys. Rev. Lett., 123:100502, 2019. DOI: 10.1103/​PhysRevLett.123.100502.

[67] I. A. Luchnikov, S. V. Vintskevich, D. A. Grigoriev, S. N. and Filippov. Machine Learning Non-Markovian Quantum Dynamics. Phys. Rev. Lett., 124:140502, 2020. DOI: 10.1103/​PhysRevLett.124.140502.

Cited by

[1] Steve Campbell and Bassano Vacchini, "Collision models in open system dynamics: A versatile tool for deeper insights?", arXiv:2102.05735.

The above citations are from SAO/NASA ADS (last updated successfully 2021-05-06 13:01:04). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2021-05-06 13:01:03).