Low-rank separable states are a set of measure zero within the set of low-rank states
Robert Lockhart · Physical Review A · 2002
It is well known that the set of separable pure states is measure zero in the set of pure states. We extend this fact and show that the set of rank-r separable states is measure 0 in the set of rank-r states provided r is less than ${\ensuremath{\prod}}_{i=1}^{p}{n}_{i}+p\ensuremath{-}\ensuremath{\sum}{n}_{i}.$