  In this article we provide a three step algorithm to obtain the Closest
Separable State to the given state in Hilbert space dimensions $2\times 2$ and
$2\times 3$, or in the higher dimensional Hilbert spaces, 'Closest Positive
Partial Transpose (PPT) state' for the chosen bipartition. In the process, a
tight lower bound to the minimum Hilbert-Schmidt distance is brought forth
together with the relation between the minimum Hilbert-Schmidt distance and
Negativity. This also leads us to discuss the validity of the said distance
from the set of separable quantum states as an entanglement measure. Any
Entanglement measure defined as the minimum of a distance measure to the set of
separable states needs to follow certain widely accepted rules. Most
significantly, contractiveness of the distance (also, CP non-expansive
property) under LOCC maps. While the Hilbert-Schmidt distance does not have
this property, it is still an open question if the measure constructed using it
is non-increasing under LOCC operations. While we outline some of the
difficulties in such a proof, we also provide numerical evidence that brings
one step closer to closing the question.
