Quantifying quantum non-Markovianity based on quantum coherence via skew information

Abstract

Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on l1 norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative α entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative α entropy of coherence are more comfortable than the original Tsallis relative α entropy of coherence for small α. I. INTRODUCTION In recent years, the Markovian and non-Markovian process for open quantum dynamics has attracted much attention. In the classical realm, the Markovian and non-Markovian dynamics are well defined and widely studied [1]. However, its quantum versions are controversial in some sense [2-5]. Various non-Markovian criteria have been proposed, and some measures are introduced based on different considerations [6-16], such as the divisibility, mutual information, information distance measures, Fisher information flow, etc. All those non-Markovianity measures do not coincide exactly in general [17-20]. Finding a universal definition for non-Markovian dynamic is an important subject in quantum information theory.Recently, a rigorous framework of quantifying coherence has been proposed, and several measures of quantum coherence are proposed [21][22][23][24][25][26][27][28], such as the l 1 -norm of coherence, relative entropy of coherence, fidelity of coherence, etc. As is well known, the Kraus operators of the phase damping channels, the amplitude channels and the random unitary channels are qubit incoherent operators, and coherence measures are monotonicity under all the incoherent completely positive and trace-preserving maps. Hence, the coherence measures are employed to investigate the detection of non-Markovianity. Chanda et al. used the l 1 -norm of coherence to define the measure of non-Markovianity, and shew that it is equivalent to the measures based on trace distance, quantum mutual information and quantum *