Operational Interpretation for Global Multipartite Entanglement

We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation. We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite entanglement measure. Using channels that depolarize across different partitions, we obtain related multipartite entanglement measures. We show that this measure is the sum of expectation values of local observables on two copies of the state.

Figure 1

Regularized quantum Fisher information as a function of the noise parameter for a locally depolarizing channel in three qubits. Left figure shows the regularized QFI for GHZ states $\sqrt{{\mu }_1}|000⟩+\sqrt{1-{\mu }_1}|111⟩$ of three qubits. The darkest line (red online) represents a separable state and the lightest line represents a maximally entangled state. Right figure shows the regularized QFI for $W$ states ${\mu }_1|100⟩+{\mu }_2|010⟩+{\mu }_2|001⟩$, with ${\mu }_2=\sqrt{(1-{\mu }_1^2)/2}$. Intermediate lines correspond to intermediate states.