One-Qubit Reduced States of a Pure Many-Qubit State: Polygon Inequalities
Atsushi Higuchi, Anthony Sudbery, Jason Szulc · Physical Review Letters · 2003
We show that a necessary and sufficient condition for a set of n one-qubit mixed states to be the reduced states of a pure n-qubit state is that their smaller eigenvalues should satisfy polygon inequalities: each of them must be no greater than the sum of the others.