  We observe at record-high speed the nonclassical nature of ultra-broadband
bi-photons, reducing the measurement time by four orders of magnitude compared
to standard techniques of Hong-Ou-Mandel interference or sum-frequency
generation. We measure the quantum state of the broadband bi-photons, amplitude
and phase, with a pairwise "Mach-Zehnder" quantum interferometer, where
bi-photons that are generated in one nonlinear crystal are enhanced
(constructive interference) or diminished (destructive interference) in another
crystal, depending on the bi-photon phase. We verify the quantum nature of the
interference by observing the dependence of the fringe visibility on internal
loss. Since destructive interference is equivalent to an attempt to annihilate
in the second crystal (by up-conversion) the bi-photons that were created in
the first crystal (by down-conversion), the fringe visibility is a measure for
the quantum bi-photon purity of the broadband light. The measurement speed-up
is due to the large homodyne-like gain from the strong pump
($\!\sim\!10^{7-9}$) in the up-conversion efficiency of single bi-photons,
which enables the use of simple photo-detection of the full, ultra-high photon
flux instead of single-photon / coincidence counting.
