Positively Divisible Non-Markovian Processes and Measuring the Degree of Quantum Non-Markovianity

Speaker: Bilal Cantürk (Albert-Ludwigs University Freiburg, Breuer Group)

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Title: Positively Divisible Non-Markovian Processes and Measuring the Degree of Quantum Non-Markovianity

Speaker: GHE Fellow Bilal Cantürk, (Albert-Ludwigs University Freiburg, Breuer Group)

Date: October 24th 2023 @ 12:15

Place: University of Basel, Departement Physik, New lecture hall 1

Abstract:

Markov Processes are generally characterized by two essential components: 1) the Chapman-Kolmogorov equation and 2) an initial probability distribution. On the other hand, a quantum Markovian process is frequently defined to be completely positively divisible, a property which is considered to be equivalent to the Chapman-Kolmogorov equation [1]. However, there are other definitions of quantum Markovianity which in general differ from the former [2, 3]. In this talk, a possible unification of these definitions will be discussed.
We have constructed a non-Markovian process which satisfies the Chapman-Kolmogorov equation by manipulating a certain Markov process [4]. Therefore, based on this fact one might argue that the property of being completely positively divisible property is not sufficient to characterize a quantum process as Markovian if there would be a way to connect the essential elements of the quantum and the classical processes to each other.

[1] A. Rivas, S. F. Huelga and M. B. Plenio, “Quantum non-Markovianity: characterization, quantification and detection,” Reports on Progress in Physics, vol. 77, p. 094001, 2014.
[2] H.-P. Breuer, E.-M. Laine, and J. Piilo, «Measure for the degree of non-Markovian behavior of quantum processes in open system, » Phys. Rev. Lett., vol. 103, p. 210401, 2009.
[3] H.-P. Breuer, E.-M. Laine, I. Piilo and B. Vacchini, “Colloquium: Non-Markovian dynamics in open quantum systems,” Rev. Mod. Phys., vol. 88, no. 2, p. 021002, 2016.
[4] B. Canturk and H.-P. Breuer, «On the consistent characterization of positively divisible non-Markovian processes, » in preparation