1207.2286 (Eyuri Wakakuwa et al.)

Chain rule implies Tsirelson's bound: an approach from a generalized
mutual information    [PDF]

Eyuri Wakakuwa, Mio Murao

To analyze the information theoretical derivation of Tsirelson's bound based on information causality, which is defined in terms of the efficiency of random access coding, we introduce a generalized mutual information between a classical system and a general probabilistic system. The generalization is based on the consideration of the classical information capacity of a general probabilistic system. We show that the chain rule of the generalized mutual information is essential for the derivation of Tsirelson's bound. By using the mutual information, we formulate a principle, which we call "no-supersignalling condition", that the assistance of nonlocal correlations does not increase the capacity of classical communication. We prove that this condition is equivalent to the no-signalling condition, and as a result, we show that information causality is essentially a matter of a single party.

View original: http://arxiv.org/abs/1207.2286