Information Causality

Abstract

We review the literature on the principle of Information Causality (IC). IC belongs to the attempts of rederiving quantum physics from physical principles. Contrary to most reconstruction theorems, which assume that some (otherwise uncharacterized) measurements provide all the available information, IC is formulated as a device-independent communication task. As such, it could only hope to recover the set of correlations predicted by quantum physics, not the Hilbert space formalism itself. The first remarkable achievement of IC was the derivation of the Tsirelson bound for the Clauser-Horne-Shimony-Holt inequality without Hilbert-space formalism. After that, other results have been obtained for bipartite scenarios, which leave the possibility open that IC may define exactly the quantum set. However, when the bipartite IC criterion is applied to multipartite scenarios, it definitely does not recover the quantum set: the possibility of a multipartite generalization of IC is one of the challenging problems that are still open. Also, since it was first proposed, the principle of IC has received refined formulations, one of which is presented here for the first time (namely, that all the results obtained previously hold if “communicating M bits of information” means “a single use of a channel with classical capacity M” instead of a simple transfer of M bits).