title: Device-independent tests of entropy.
abstract: We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical communication, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.
authors.affiliation: Institute for Physics & FDM, University of Freiburg, 79104 Freiburg, Germany.|Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany.
authors.forename: Rafael
authors.initials: R
authors.lastname: Chaves
authors.affiliation: Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
authors.forename: Jonatan Bohr
authors.initials: JB
authors.lastname: Brask
authors.affiliation: Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Brunner