  Non-Markovian effects in open quantum system dynamics usually manifest
backflow of information from the environment to the system, indicating
complete-positive divisibility breaking of the dynamics. We provide a criterion
for witnessing such non-Markovian dynamics exhibiting information backflow,
based on the moments of Choi-matrices. The moment condition determined by the
positive semi-definiteness of a matrix, does not hold for a Choi-state
describing non-Markovian dynamics. We then present some explicit examples in
support of our proposed non-Markovianity detection scheme. Finally, a moment
based measure of non-Markovianity for unital dynamics is formulated.
