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 / with respect to a distribution μ is Disc_μf, then any two party randomized protocol computing f must reveal at least Ω(log(1/Disc_μf)) 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 × {0,1}~n must reveal Ω(n) bits of information to the participants. In addition, we prove that the discrepancy of the Greater-Than function is Ω(1~(1/2)), which provides an alternative proof to the recent proof of Viola [Violl] of the Ω(log n) lower bound on the communication complexity of this well-studied function and, combined with our main result, proves the tight Ω(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. [KLL~+12], this simulation procedure was a building block towards a proof that almost all known lower bound techniques for communication complexity (and not just discrepancy) apply to information complexity.
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