In our most recent publication for the special issue on nonlocality of the Journal of Entropy, we study Bell scenarios supplemented by one bit of communication. The main motivation is to close a longstanding open problem concerning the communication complexity of quantum correlations.
The problem is the following: “Can the statistics obtained by performing projective measurements on two-qubit states be reproduced through the communication of one bit between the parties?”. We study the case of three projective measurements for each party and show that quantum statistics can be reproduced in this scenario, in the worst cases by sending one bit at least half of the time. Our results also expose a general structure behind the facet inequalities of Bell scenarios with an added bit of communication, based on the facet inequalities of the (communication-less) Bell scenarios.