can use these two states indistintively for exactly the same tasks. It is a celebrated result [@Be95] that, when applied to many copies of a state, this criterion leads to identifying all bipartite pure-state entanglement with that of the EPR state $1/\sqrt{2}({\mbox{$| 00 \rangle$}}+{\mbox{$| 11 \rangle$}}) $[@Ei35]. That is, the entanglement of any pure state ${\mbox{$| \psi \rangle$}}_{AB}$ is asymptotically equivalent, under deterministic LOCC, to that of the EPR state, the entropy of entanglement $E(\psi_{AB})$ —the entropy of the reduced density matrix of either system $A$ or $B$— quantifying the amount of EPR entanglement contained asymptotically in ${\mbox{$| \psi \rangle$}}_{AB}$. In contrast, recent contributions have shown that in systems shared by three or more parties there are several inequivalent forms of entanglement under asymptotic LOCC [@asy; @Be99].

This paper is essentially concerned with the entanglement properties of a single copy of a state, and thus asymptotic results do not apply here. For single copies it is known that two pure states ${\mbox{$| \psi \rangle$}}$ and ${\mbox{$| \phi \rangle$}}$ can be obtained with certainty from each other by means of LOCC if and only if they are related by local unitaries LU [@Vi00J; @Be99]. But even in the simplest bipartite systems, 