Non-Markovianity and memory effects in quantum open systems
S. C. Hou, Shiuan-Ni Liang, X. X. Yi · Physical Review A · 2015
Although a number of measures for quantum non-Markovianity have been proposed recently, it is still an open question whether these measures directly characterize the memory effect of the environment, i.e., the dependence of a quantum state on its past in a time evolution. In this paper, we present a criterion and propose a measure for non-Markovianity with clear physical interpretations of the memory effect. The non-Markovianity is defined by the inequality $T({t}_{2},{t}_{0})\ensuremath{ e}T({t}_{2},{t}_{1})T({t}_{1},{t}_{0})$ in terms of memoryless dynamical map $T$ introduced in this paper. This definition is conceptually distinct from that based on divisibility used by Rivas et al. [Phys. Rev. Lett. 105, 050403 (2010)], whose violation is manifested by noncomplete positivity of the dynamical map. We demonstrate via a typical quantum process that without Markovian approximation, nonzero memory effects (non-Markovianity) always exist even if the non-Markovianity is zero by the other non-Markovianity measures.