Tsirelson's Bound Prohibits Communication Through a Disconnected Channel

Why does nature only allow nonlocal correlations up to Tsirelson's bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson's bound is violated. This provides a statistical justification for Tsirelson's bound on nonlocal correlations in a bipartite setting.Comment: 9 pages, 2 figures. Title and abstract modified, exposition simplifie