We show that Breuer-Laine-Piilo (BLP) non-Markovianity cannot capture the dynamical information in the non-unital aspect of the quantum dynamics. Moreover, we provide a measure on the effect of the non-unitality of quantum processes on the infinitesimal non-divisibility. This measure can be used as a supplement to BLP non-Markovianity for non-unital quantum processes. A measure on the degree of the non-unital behavior of quantum processes is also given in this paper.
@article{arxiv.1301.5763,
title = {Non-unital non-Markovianity of quantum dynamics},
author = {Jing Liu and Xiao-Ming Lu and Xiaoguang Wang},
journal= {arXiv preprint arXiv:1301.5763},
year = {2013}
}