a quantitative description of the non-local resources contained in a single copy of a two-qubit pure state [@monotones]. Any state ${\mbox{$| \psi \rangle$}}$ can be obtained from state (\[EPR\]) with certainty, this contributing to the fact that the EPR state is considered the maximally entangled state of two qubits.

Entanglement of pure states of three qubits
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In this section we analyze a system of three qubits. We show that SLOCC split the set of pure states into 6 inequivalent classes, which further structure themselves into a three-grade hierarchy when non-invertible local operations are used to relate them. At the top of the hierarchy we find two inequivalent classes of true tripartite entanglement, which we name GHZ-class and W-class after our choice of corresponding representatives. The three possible classes of bipartite entanglement are accessible (with some non-vanishing probability) from [*any*]{} state of the W and GHZ classes by means of a non-invertible local operator. Finally, at the bottom of the hierarchy we find non-entangled states.

The ranks r$(\rho_A)$, r$(\rho_B)$ and r$(\rho_C)$ of the reduced density matrices, together with the range $R(\rho_{BC})$ of $\rho_{BC}$, will be the main mathematical tools used through the first part of this section. By analysing them 