Abstract

We identify a set of dynamical maps of open quantum system, and refer to them as" -Markovian" maps. It is constituted of maps that possibly violate Markovianity but only a" little". We characterize the" -nonmarkovianity" of a general dynamical map by the minimum distance of that map from the set of -Markovian maps. We analytically derive an inequality which gives a bound on the -nonmarkovianity of the dynamical map, in terms of an entanglement-like resource generated between the system and its" immediate" environment. In the special case of a vanishing , this inequality gives a relation between the non-Markovianity of the reduced dynamical map on the system and the entanglement generated between the system and its immediate environment. We investigate the behavior of the measures for classes of amplitude damping and phase damping channels.

Abstract

A master equation has been constructed for a global system–bath interaction in the both absence and presence of non-Markovian noise. For the memoryless case, it has been exactly solved for a paradigmatic class of two qubit states in high- and zero-temperature thermal environment. For the non-Markovian model, it has been solved for zero-temperature bath. The evolution of quantum coherence and entanglement has been observed in the presence of the above-mentioned interactions. We show that the global part of the system–bath interaction compensates for the decoherence, resulting in slowdown of coherence and entanglement decay. For an appropriately defined limiting case, both coherence and entanglement show freezing behavior for the high-temperature bath. In case of zero-temperature bath, the mentioned interaction not only stabilizes the non-classical correlations, but also enhances them …