Is entanglement sufficient to quantify quantum non-locality? - Gilad Gour

I will show that a finite number of conditions are {\em not} sufficient to determine the locality of transformations between two $d\times d$ mixed states with $d\geq 4$, as well as the locality of transformations between two probability distributions of pure states. A natural question is then arise: is an infinite number of conditions sufficient? In other words, is entanglement sufficient to quantify non-locality in quantum mechanics? As a simple example, I will present an infinite, but minimal, set of necessary and sufficient conditions for the existence of a local procedure that converts one probability distribution of two pure pair of qubits into another.