The purity of any absolutely PPT bipartite state in dimension m by n is bounded above by a piecewise formula near 4/(3mn), tight for qubit-qudit systems when mn is at least 8.
Johnston,Separability from spectrum for qubit-qudit states, Phys
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An upper bound for the purity of absolutely positive partial transpose states
The purity of any absolutely PPT bipartite state in dimension m by n is bounded above by a piecewise formula near 4/(3mn), tight for qubit-qudit systems when mn is at least 8.