Alternative non-Markovianity measure by divisibility of dynamical maps

Abstract

Identifying non-Markovianity with non-divisibility, we propose a measure for non-Markovinity of quantum process. Three examples are presented to illustrate the non-Markovianity, measure for nonMarkovianity is calculated and discussed. Comparison with other measures of non-Markovianity is made. Our non-Markovianity measure has the merit that no optimization procedure is required and it is finite for any quantum process, which greatly enhances the practical relevance of the proposed measure.

Unification of witnessing initial system-environment correlations and witnessing non-Markovianity

“…However, checking for all times has practical difficulties. Other witnesses of non-Markovianity admit this difficulty by testing for non-Markovianity only for a specific time interval [8,34]. We will now consider another related witness: given some time t, if N > 0, then the process is non-Markovian.…”

“…The strong version of the witness required to check for N (t) > 0 for all −∞ t ∞. Since completely positive maps are contractive, applying this witness for an interval of time is equivalent to witnessing the property known as P-divisibility [34,52]. This strong witness requires us to examine both M(t) and C(t) for all time −∞ t ∞.…”

“…-A witness, W, of some property, w, is a mathematical object such that: If W > 0, then the property w is satisfied. Some of the non-Markovianity witnesses have focused on detecting deviations from completely positive dynamics as a feature of non-Markovianity [8,34], a property called divisibility. Others have focused on detecting deviations from contractive dynamics as witnesses of non-Markovianity [8,9,11,12,[35][36][37][38].…”

Non-Markovianity and initial correlations for the generalized Lindblad master equation

“…A natural question is: what are the differences between Markovian and non-Markovian processes, and how can we quantitate the non-Markovianity in open quantum systems. This problem has been studied recently and several methods have been proposed from considering different aspects of the system [4][5][6][7][8][9][10][11][12][13][14][15][16]. For example, in Ref.…”

“…In Refs. [9] and [10], measures are constructed based on the idea of composition law, which is equivalent to divisibility. Based on the trace distance, Breuer and his collaborators have proposed a scheme through the quantification of the flow of information between the open system and its environment [4,5].…”