  Master equations in the Lindblad form describe evolution of open quantum
systems that is completely positive and simultaneously has a semigroup
property. We analyze a possibility to derive this type of master equations from
an intrinsically discrete dynamics that is modelled as a sequence of collisions
between a given quantum system (a qubit) with particles that form the
environment. In order to illustrate our approach we analyze in detail how a
process of an exponential decay and a process of decoherence can be derived
from a collision-like model in which particular collisions are described by
SWAP and controlled-NOT interactions, respectively.
