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It is shown that a finite number of conditions are {\em not} sufficient todetermine the locality of transformations between two probability distributionsof pure states as well as the locality of transformations between two $d\timesd$ mixed states with $d\geq 4$. As an example, an infinite, but minimal, set ofnecessary and sufficient conditions for the existence of a local procedure thatconverts one probability distribution of two pure pair of qubits into anotherone is found.Comment: 4 page

Infinite number of conditions for local mixed-state manipulations