The Role of the Total Entropy Production in the Dynamics of Open Quantum Systems in Detection of Non-Markovianity

Abstract

In the theory of open quantum systems interaction is a fundamental concepts in the review of the dynamics of open quantum systems. Correlation, both classical and quantum one, is generated due to interaction between system and environment. Here, we recall the quantity which well known as total entropy production. Appearance of total entropy production is due to the entanglement production between system an environment. In this work, we discuss about the role of the total entropy production for detecting non-Markovianity. By utilizing the relation between total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity.

Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity

“…There are several works that look for manifestation of non-Markovianity in the non-monotonic behavior of a number of other quantum-mechanical properties of a system, e.g. flow of quantum Fisher information [8], fidelity difference [9], quantum mutual information [10], volume of accessible states of a system [11], accessible information [12], total entropy production [13], quantum interferometric power [14], coherence [15], etc. Another class of measures, proposed by Breuer et al [16] (see also [17]), associates the distinguishability of quantum states with the non-Markovian behavior of their evolution.…”

Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity

“…There are several works that looks for manifestation of non-Markovianity in the non-monotonic behaviour of a number of other quantummechanical properties of a system, e.g. flow of quantum Fisher information [6], fidelity difference [7], quantum mutual information [8], volume of accessible states of a system [9], accessible information [10], total entropy production [11], quantum interferometric power [12], coherence [13], etc. Another class of measures, proposed by Breuer et al [14], associates the distinguishability of quantum states with the non-Markovian behavior of their evolution.…”