  Information causality states that the information obtainable by a receiver
cannot be greater than the communication bits from a sender, even if they
utilize no-signaling resources. This physical principle successfully explains
some boundaries between quantum and post-quantum nonlocal correlations, where
the obtainable information reaches the maximum limit. We show that no-signaling
resources of pure partially entangled states produce randomness (or noise) in
the communication bits, and achievement of the maximum limit is impossible,
i.e., the information causality principle is insufficient for the full
identification of the quantum boundaries already for bipartite settings. The
nonlocality inequalities such as so-called the Tsirelson inequality are
extended to show how such randomness affects the strength of nonlocal
correlations. As a result, a relation followed by most of quantum correlations
in the simplest Bell scenario is revealed. The extended inequalities reflect
the cryptographic principle such that a completely scrambled message cannot
carry information.
