Tsirelson’s Bound Prohibits Communication through a Disconnected Channel

Abstract

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.

Keywords

• nonlocality
• Bell inequality
• Tsirelson’s bound
• no-signaling
• information causality
• Fisher information