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. $P^{(bos)}P^{(ferm)}$ is observed. Such effect is exemplified by considering the passive $\mathcal{PT}$-symmetric optical directional coupler.