Non-Markovianity Measure Based on Brukner–Zeilinger Invariant Information for Unital Quantum Dynamical Maps

Abstract

A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information.

Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility

“…Incoherent and Unital dynamics.− A number of measures of non-Markovianity were suggested for incoherent and unital dynamics [39][40][41], which are not nonincreasing under arbitrary CPTP maps. Therefore, they are not guaranteed to be monotonically decreasing under arbitrary CPD dynamics, which are well accepted Markovian dynamics.…”

Effect of entanglement embedded in environment on quantum non-Markovianity based on collision model

“…Various methods for the measure of non-Markovianity have been proposed [22][23][24][25][26][27][28][29][30][31]. In our work, we adopt the BLP measure proposed in [29], which can be expressed as…”

“…In other words, the system can retrieve some information lost during the evolution of the system. In recent years, the study of non-Markovian dynamics has attracted extensive attentions and becomes a topical field [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], particularly in the characterization and measure of non-Markovianity [22][23][24][25][26][27][28][29][30][31]. For example, the Breuer, Laine, and Piilo (BLP) measure [29] is proposed based on the trace distance which quantifies the degree of distinguishability between two arbitrary different initial states.…”