  It is shown that a finite number of conditions are {\em not} sufficient to
determine the locality of transformations between two probability distributions
of pure states as well as the locality of transformations between two $d\times
d$ mixed states with $d\geq 4$. As an example, 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
one is found.
