  This paper provides the first general technique for proving information lower
bounds on two-party unbounded-rounds communication problems. We show that the
discrepancy lower bound, which applies to randomized communication complexity,
also applies to information complexity. More precisely, if the discrepancy of a
two-party function $f$ with respect to a distribution $\mu$ is $Disc_\mu f$,
then any two party randomized protocol computing $f$ must reveal at least
$\Omega(\log (1/Disc_\mu f))$ bits of information to the participants. As a
corollary, we obtain that any two-party protocol for computing a random
function on $\{0,1\}^n\times\{0,1\}^n$ must reveal $\Omega(n)$ bits of
information to the participants.
  In addition, we prove that the discrepancy of the Greater-Than function is
$\Omega(1/\sqrt{n})$, which provides an alternative proof to the recent proof
of Viola \cite{Viola11} of the $\Omega(\log n)$ lower bound on the
communication complexity of this well-studied function and, combined with our
main result, proves the tight $\Omega(\log n)$ lower bound on its information
complexity.
  The proof of our main result develops a new simulation procedure that may be
of an independent interest. In a very recent breakthrough work of Kerenidis et
al. \cite{kerenidis2012lower}, this simulation procedure was the main building
block for proving that almost all known lower bound techniques for
communication complexity (and not just discrepancy) apply to information
complexity.
