The signaling dimension of physical systems

Abstract

The signaling dimension of a physical system is the minimum dimension of a classical channel that can reproduce the set of input-output correlations attainable by the given system. Here we put the signaling dimension into perspective by reviewing some of the main known results on the topic, starting from Frenkel and Weiner's 2015 breakthrough showing that the signaling dimension of any quantum system is equal to its Hilbert space dimension.