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Information Causality contributes to the program of deriving fundamentals ofquantum theory from information theoretic principles. It puts restrictions onthe amount of information learned by a party (Bob) from the other party (Alice)in a one-way communication scenario: Bob receives an index b, and after aone-way communication from Alice, tries to recover the b-th bit of Alice'sinput. In this manuscript we note that Information Causality is indeed a pointin the dual of the Gray-Wyner region in the case where Alice's input bits arechosen independently at random. The main motivation of this work was to studythis connection in the case of correlated input bits. Our approach to forgethis connection was to propose a new postulate called Accessibility of MutualInformation (AMI) on the underling physical theory. This approach, explained inthe first version of this paper, fails since AMI is not satisfied by thequantum theory.

Information Causality is a Special Point in the Dual of the Gray-Wyner Region