Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement.

Figure 1

To discriminate the pure states $\{|{\phi }_i⟩{\}}_{i=1}^N$ perfectly under LOCC, the sum of the entanglement “distances” $E(|{\phi }_i⟩)$ must be less than the total dimension $D$ (theorems 1 and 2); thus, $N\le D/\overline{E(|{\phi }_i⟩)}$.