Universality of generalized bunching and efficient assessment of Boson Sampling

It is found that $N$ identical bosons (fermions) show generalized bunching (antibunching) in $1\le \K\le M-1$ output modes of a random $M$-mode linear network: The maximum (minimum) probability of detecting all input particles in $\K$ output modes is attained only when the bosons (fermions) are completely indistinguishable. For fermions $\K$ is arbitrary, for bosons it is either ($i$) arbitrary for only classically correlated particles or ($ii$) satisfies $\K\ge N$ (or $\K=1$) for arbitrary input states. The generalized bunching supplies an efficient assessment protocol of Boson Sampling with an \textit{arbitrary network}, which requires only a polynomial number of runs of experimental device and computation of only one matrix permanent of a positive definite Hermitian matrix (with a value close to 1), with an analytic formula for the Scattershot version of Boson Sampling.