  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 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.
