  We discover novel transitions characterized by distinguishability of bosons
in non-unitary dynamics with parity-time ($\mathcal{PT}$) symmetry. We show
that $\mathcal{PT}$ symmetry breaking, a unique transition in non-Hermitian
open systems, enhances regions in which bosons can be regarded as
distinguishable. This means that classical computers can sample the boson
distributions efficiently in these regions by sampling the distribution of
distinguishable particles. In a $\mathcal{PT}$-symmetric phase, we find one
dynamical transition upon which the distribution of bosons deviates from that
of distinguishable particles, when bosons are initially put at distant sites.
If the system enters a $\mathcal{PT}$-broken phase, the threshold time for the
transition is suddenly prolonged, since dynamics of each boson is diffusive
(ballistic) in the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase.
Furthermore, the $\mathcal{PT}$-broken phase also exhibits a notable dynamical
transition on a longer time scale, at which the bosons again become
distinguishable. This transition, and hence the classical easiness of sampling
bosons in long times, are true for generic postselected non-unitary quantum
dynamics, while it is absent in unitary dynamics of isolated quantum systems.
$\mathcal{PT}$ symmetry breaking can also be characterized by the efficiency of
a classical algorithm based on the rank of matrices, which can (cannot)
efficiently compute the photon distribution in the long-time regime of the
$\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase.
