Quantum statistical signature of $\mathcal{PT}$ symmetry breaking

In multiparticle quantum interference, bosons show rather generally the tendency to bunch together, while fermions can not. This behavior, which is rooted in the different statistics of the particles, results in a higher coincidence rate $P$ for fermions than for bosons, i.e. $P^{(bos)}<P^{(ferm)}$. However, in lossy systems such a general rule can be violated because bosons can avoid lossy regions. Here it is shown that, in a rather general optical system showing passive parity-time ($\mathcal{PT}$) symmetry, at the $\mathcal{PT}$ symmetry breaking phase transition point the coincidence probabilities for bosons and fermions are equalized, while in the broken $\mathcal{PT}$ phase the reversal $P^{(bos)}>P^{(ferm)}$ is observed. Such effect is exemplified by considering the passive $\mathcal{PT}$-symmetric optical directional coupler.