Universality of Generalized Bunching and Efficient Assessment of Boson Sampling

It is found that identical bosons (fermions) show generalized bunching (antibunching) property in linear networks: The absolute maximum (minimum) of probability that all $N$ input particles are detected in a subset of $\mathcal{K}$ output modes of any nontrivial linear $M$-mode network is attained $\mathit{\text{only}}$ by completely indistinguishable bosons (fermions). For fermions $\mathcal{K}$ is arbitrary, for bosons it is either ($i$) arbitrary for only classically correlated bosons or ($ii$) satisfies $\mathcal{K}\ge N$ (or $\mathcal{K}=1$) for arbitrary input states of $N$ particles. The generalized bunching allows to certify in a $\mathit{\text{polynomial}}$ in $N$ number of runs that a physical device realizing Boson Sampling with \textit{an arbitrary} network operates in the regime of full quantum coherence compatible $\mathit{\text{only}}$ with completely indistinguishable bosons. The protocol needs $\mathit{\text{only}}\mathit{\text{polynomial}}$ classical computations for the standard Boson Sampling, whereas an $\mathit{\text{analytic}}\mathit{\text{formula}}$ is available for the scattershot version.