  Advanced quantum technologies, as well as fundamental tests of quantum
physics, crucially require the interference of multiple single photons in
linear-optics circuits. This interference can result in the bunching of photons
into higher Fock states, leading to a complex bosonic behaviour. These
challenging tasks timely require to develop collective criteria to benchmark
many independent initial resources. Here we determine whether n independent
imperfect single photons can ultimately bunch into the Fock state $|n \rangle$.
We thereby introduce an experimental Fock-state bunching capability for
single-photon sources, which uses phase-space interference for extreme bunching
events as a quantifier. In contrast to autocorrelation functions, this
operational approach takes into account not only residual multi-photon
components but also vacuum admixture and the dispersion of the individual
photon statistics. We apply this approach to high-purity single photons
generated from an optical parametric oscillator and show that they can lead to
a Fock-state capability of at least 14. Our work demonstrates a novel
collective benchmark for single-photon sources and their use in subsequent
stringent applications.
