Distinguishability transitions in nonunitary boson-sampling dynamics

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