Information Causality is a Special Point in the Dual of the Gray-Wyner Region
arXiv:1111.3151
Abstract
Information Causality contributes to the program of deriving fundamentals of quantum theory from information theoretic principles. It puts restrictions on the 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 a one-way communication from Alice, tries to recover the b-th bit of Alice's input. In this manuscript we note that Information Causality is indeed a point in the dual of the Gray-Wyner region in the case where Alice's input bits are chosen independently at random. The main motivation of this work was to study this connection in the case of correlated input bits. Our approach to forge this connection was to propose a new postulate called Accessibility of Mutual Information (AMI) on the underling physical theory. This approach, explained in the first version of this paper, fails since AMI is not satisfied by the quantum theory.
2 pages, Includes the main setting of the problem, a brief description of our solution and why it fails. Some of the results are moved to arXiv:1207.3911. See the first version on arXiv for details