as their representatives the state (\[maxi\]) with $n_{\psi}=1,...,n$. Clearly $n_{\psi}=1$ corresponds to states that are less entangled than the rest (they are, after all, unentangled). This hierarchical relation can be extended to the rest of classes by noting that none-invertible local operators can project out some of the Schmidt terms and thus diminish the Schmidt number of a state. Therefore the state ${\mbox{$| \psi \rangle$}}$ can be locally converted into the state ${\mbox{$| \phi \rangle$}}$ with some finite probability iff $n_{\psi}\geq n_{\phi}$, or in terms of kinds of entanglement, we can say that the entanglement of the class characterized by a given Schmidt number is more powerful than that of a class with a smaller Schmidt number.

For later reference we also note that in a two-qubit system, $\H=\C^2\otimes\C^2$, we can write any state, after using a convenient LU, uniquely as = c\_  + s\_  ;      c\_ s\_0, where $c_{\delta}, s_{\delta}$ stand for cos$\delta$ and sin$\delta$. This is either a product (unentangled) state ${\mbox{$| \psi_{A-B} \rangle$}}={\mbox{$| 0 \rangle$}}\otimes {\mbox{$| 0 \rangle$}}$ for $c_{\delta}=1$ or else an entangled state that can be converted into the EPR state, (+), \[EPR\] with probability $p=E_{2}(\psi)$, where $E_2(\psi)\equiv \lambda_2$ is the entanglement monotone that provides 