Infinite number of conditions for local mixed state manipulations
Abstract
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× d mixed states with d≥ 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.
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