  The Pearson correlation, correlation ratio, and maximal correlation have been
well-studied in the literature. In this paper, we study the conditional
versions of these quantities. We extend the most important properties of the
unconditional versions to the conditional versions, and also derive some new
properties. Based on the conditional maximal correlation, we define an
information-correlation function of two arbitrary random variables, and use it
to derive an impossibility result for the problem of the non-interactive
simulation of random variables.
