Infinite number of conditions for local mixed-state manipulations
Gilad Gour · Physical Review A · 2005
It is shown that a finite number of conditions are not sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two $d\ifmmode\times\else\texttimes\fi{}d$ mixed states with $d\ensuremath{\geqslant}4$. 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.