  Non-Markovian dynamics detection is one of the most popular subjects in the
quantum information science. In this paper, a linear-entropy-based
non-Markovianity witness scheme is constructed. The positive definiteness of
the Choi state will be broken in the non-Markovian evolution, which can be
witnessed by its linear entropy. Thus, the linear entropy of the Choi state can
be used to witness the non-Markovian dynamics. The effectiveness of the
proposed method is verified by an example of the pure dephasing channel. Also,
it is shown that this method can be extended to the one based on R\'enyi
entropy.
