  Despite their factor of ~10^8 difference in black hole mass, several lines of
evidence suggest possible similarities between black hole accretion flows in
active galactic nuclei (AGN) and Galactic X-ray binaries. However, it is still
unclear whether the geometry of the disk-corona system in X-ray binaries
directly scale up to AGN, and whether this analogy still holds in different
accretion states. We test this AGN/X-ray binary analogy, by comparing the
observed correlations between the UV-to-X-ray spectral index (alpha_OX) and
Eddington ratio in AGN to those predicted from observations of X-ray binary
outbursts. This approach probes the geometry of their disk-corona systems as
they transition between different accretion states. We use new Chandra X-ray
and ground-based rest-UV observations of faded 'changing-look' quasars to
extend this comparison to lower Eddington ratios of <10^-2, where observations
of X-ray binaries predict a softening of alpha_OX in AGN. We find that the
observed correlations between alpha_OX and Eddington ratio of AGN displays a
remarkable similarity to accretion state transitions in prototypical X-ray
binary outbursts, including an inversion of this correlation at a critical
Eddington ratio of ~10^-2. Our results suggest that the structures of black
hole accretion flows directly scale across a factor of ~10^8 in black hole mass
and across different accretion states, enabling us to apply theoretical models
of X-ray binaries to explain AGN phenomenology.
