  The entanglement dynamics in a non-Hermitian quantum system is studied
numerically and analyzed from the viewpoint of quasiparticle picture. As a
concrete model, we consider a one-dimensional tight-binding model with
asymmetric hopping (Hatano-Nelson model) under onsite disorder and
nearest-neighbor interaction. As opposed to an assertion of previous studies,
the entanglement dynamics in this non-Hermitian quantum system is very
different from the one in its Hermitian counterpart, especially in the
delocalized regime with weak disorder; there the entanglement entropy $S_{\rm
ent}(t)$ shows a characteristic non-monotonic time evolution. We have clarified
and quantified the nature of this behavior in the quasiparticle picture. In the
asymptotic regime of $t\rightarrow\infty$, the entanglement entropy $S_{\rm
ent}(t)$ in this regime saturates to a much suppressed value, which increases
only logarithmically with respect to the size of the subsystem.
