Entanglement measures and the Hilbert-Schmidt distance
Ozawa, M · CERN Document Server (European Organization for Nuclear Research) · 2000
In order to construct a measure of entanglement on the basis of a``distance'' between two states, it is one of desirable properties that the``distance'' is nonincreasing under every completely positive trace preservingmap. Contrary to a recent claim, this letter shows that the Hilbert-Schmidtdistance does not have this property.