  The quantum correlation of octave-spanning time-energy entangled bi-photons
can be as short as a single optical cycle. Many experiments designed to explore
and exploit this correlation require a uniform spectral phase
(transform-limited) with very low loss. So far, transform-limited single-cycle
bi-photons were not demonstrated, primarily due to lack of precision control of
the spectral phase. Here, we demonstrate precise correction of the
spectral-phase of near-octave bi-photons to less than ($<\pi/20$) (residual
phase) over nearly a full octave in frequency ($\approx1330-2600$ nm). Using a
prism-pair with an effectively-negative separation, we obtain tuned, very
low-loss compensation of both the 2nd and 4th dispersion orders. We verify the
bi-photons spectral phase directly, using a non-classical bi-photon
interference effect.
