Monogamy of Information Causality

We consider the information causality in the multi-receiver random access codes. Therein, no receiver can gain any information only from classical communication. We claim the following statement. Information causality still holds even with the help of the multi-partite physical non-local resource. That is, the summation of all revivers' information gain cannot be greater than the amount of classical communication. The distributive multi-party physical nonlocal resource can be exploited only for information splitting. It is proved that such trade-off leads to the monogamy of entanglement. Finally the connection between information causality and spin-glass Bethe lattice is discussed.