| （英） |
The framework of generalized probabilistic theories, or GPTs for short, represents the generalization of quantum theory adopted in the study of quantum foundations. In particular, GPTs are pivotal in the quantum reconstruction program, that is, the research program aimed at signing out quantum theory, among the set of all GPTs, based on operational, as opposed to merely mathematical, axioms. An important feature of any given physical system, as described by the corresponding GPT, is its signaling dimension, that quantifies the cost of its classical simulation or, more precisely, the minimal dimension of a classical system capable of reproducing all the input/output correlations of the given system. Despite its fundamental role, the signaling dimension, beyond classical and quantum theories, is known only for a very limited number of systems and GPTs. Here, we address the question what the effect would be on the signaling dimension if the Bloch sphere, that is the set of states of the elementary system in quantum theory, was replaced by a polytope. To answer this question, we improve and extend analytical and algorithmic techniques for the exact computation of the signaling dimension of any given system of any given GPT. As applications, we consider the class of rational regular and quasi-regular polytopes and their duals. |