A Simple Relation between Non-locality and a Corrected Entropy

Within the framework of a statistical interpretation of quantum mechanics entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell’s inequality Δ≤2. How do these different viewpoints match? We employ a corrected von Neumann entropy to measure the (mathematical) degree of entanglement and show that, at least in the case of 2×2 dimensions, this function is directly related to Bell’s correlation function Δ. This relation can be well approximated by an ellipse equation which, for the first time, allows for a direct comparison of the two faces of entanglement.