Information-theoretic metric as a tool to investigate nonclassical correlations

Abstract

In this paper we study an application of an information-theoretic distance between two measurements to investigate nonclassical correlations. We postulate the triangle principle, which states that any information-theoretic distance is valid for any sets of measurements, regardless if they can be jointly measured or not. As a consequence, the triangle inequality for this distance is obeyed for any three measurements. This simple principle is valid in any classical realistic theory, however, it may not hold in quantum theory. It leads to the derivation of certain inequalities whose violations are an indicator of nonclassicality. Some of these inequalities formally look the same as those found in the literature on local realism and noncontextuality, but we also derive completely different inequalities. We also show that our geometrical approach naturally implies monogamy of nonclassical correlations. © 2014 American Physical Society.