  Here we argue that the probability that a given source produces exactly a
single photon is a natural quantity to benchmark single-photon sources as it
certifies the absence of multi-photon components and quantifies the efficiency
simultaneously. Moreover, this probability can be bounded simply from an
auto-correlation measurement -- a balanced beam splitter and two photon
detectors. Such a bound gives access to various non-classicality witnesses that
can be used to certify and quantify Wigner-negativity, in addition to
non-Gaussianity and P-negativity of the state produced by the source. We
provide tools that can be used in practice to account for an imperfect beam
splitter, non-identical and non-unit detection efficiencies, dark counts and
other imperfections, to take finite statistical effects into account without
assuming that identical states are produced in all rounds, and optionally allow
one to remove the detector inefficiencies from the analysis. We demonstrate the
use of the proposed benchmark, non-classicality witness and measure using a
heralded single-photon source based on spontaneous parametric down-conversion.
We report on an average probability that a single photon is produced $\geq
55\%$ and an average measure of the Wigner negativity $\geq 0.004$ with a
confidence level of $1-10^{-10}$.
