Operational Multipartite Entanglement Measures

We introduce two operational entanglement measures that are applicable for arbitrary multipartite (pure or mixed) states. One of them characterizes the potentiality of a state to generate other states via local operations assisted by classical communication and the other characterizes the simplicity of generating the state at hand. We show how these measures can be generalized to two classes of entanglement measures. Moreover, we compute the new measures for pure few-partite systems and use them to characterize the entanglement contained in a three-qubit state. We identify the Greenberger-Horne-Zeilinger and $W$ state as the most powerful pure three-qubit states regarding state manipulation.

Figure 1

Any state $|\mathrm{\Psi }(\overrightarrow{x})⟩$ is uniquely represented by $\overrightarrow{x}$ in the interior of the simplex ${\mathcal{S}}_3$. The source (tetrahedron) and the accessible (cuboid) volume of $|\mathrm{\Psi }(\overrightarrow{x})⟩$ are depicted. The light surface corresponds to the states in the MES. Biseparable (fully separable) states, for which exactly one (at least two) $x_i$ is (are) zero, are represented by points on the white surface of ${\mathcal{S}}_3$, respectively.

Figure 2

The source (shaded volume) and accessible (cuboid) volume of the state $|\mathrm{\Psi }⟩$ with parameters $g_1=0.22$, $g_2=0.26$, $g_3=0.32$, and $z=0.1e^{i2.68}$ are depicted. The states in the MES, which fulfill condition (ii), are on the light area.