Information Causality without Concatenation

Information causality is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of nonlocal correlations. This principle can be used to bound the nonlocality of quantum mechanics without resorting to its full formalism, with a notable example of reproducing the Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality. Despite being promising, the latter result found little generalization to other Bell inequalities because of the limitations imposed by the process of concatenation, in which several nonsignaling resources are put together to produce tighter bounds. In this work, we show that concatenation can be successfully replaced by limits on the communication channel capacity. It allows us to rederive and, in some cases, significantly improve all the previously known results in a simpler manner and apply the information causality principle to previously unapproachable Bell scenarios.

Figure 1

Bound on $p$ as a function of $p_c$ characterizing binary symmetric channel. $p\to p_Q$ as $p_c\to \frac{1}{2}$.