Quantum Markov semigroups for continuous-time open quantum random walk

Open quantum random walks in Attal et al. (Phys Lett A 376:1545–1548, 2012) are quantum generalizations of classical Markov chains. In this paper, we firstly consider a problem to construct a quantum Markov semigroup (QMS) $T_t$ directly from a continuous-time open quantum random walk (CTOQRW) developed in Pellegrini (J Stat Phys 154(3):838–865, 2014) and characterize its generator as well as its predual semigroup $T_{\ast t}$. We show that this type of CTOQRWs brings about a large field of exploration for the behavior of open quantum system. Finally, we discuss some properties of this type of QMS constructed from CTOQRWs.