  Active galactic nuclei (AGN) are a promising source for high-energy
astrophysical neutrinos (HEANs). By the end of 2022, the Vera C. Rubin
Observatory (VRO) will begin to observe $\gtrsim10$ million AGN with a regular
and high cadence. Here, we evaluate the capacity of VRO, in tandem with various
current and upcoming neutrino telescopes, to establish AGN as HEAN emitters. To
do so, we assume that the neutrino luminosity from any given AGN at any given
time is proportional to the electromagnetic luminosity. We then estimate the
error with which this fraction can be measured through spatial and temporal
cross-correlation of VRO light curves with IceCube, KM3NeT, and Bakail-GVD. We
find that it may be possible to detect AGN contributions at the $\sim3 \sigma$
level to the HEAN flux even if these AGN contribute only $\sim10\%$ of the HEAN
flux. The bulk of this information comes from spatial correlations, although
the temporal information improves the sensitivity a bit. The results also imply
that if an angular correlation is detected with high signal-to-noise, there may
be prospects to detect a correlation between AGN variability and neutrino
arrival times. The small HEAN fraction estimated here to be accessible to the
entirety of the VRO AGN sample suggests that valuable information on the
character of the emitting AGN may be obtained through similar analyses on
different sub-populations of AGN.
