Device-Independent Detection of Genuine Multipartite Entanglement for All Pure States

We show that genuine multipartite entanglement of all multipartite pure states in arbitrary finite dimension can be detected in a device-independent way by employing bipartite Bell inequalities on states that are deterministically generated from the initial state via local operations. This leads to an efficient scheme for large classes of multipartite states that are relevant in quantum computation or condensed-matter physics, including cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model. For cluster states the detection of genuine multipartite entanglement involves only measurements on a constant number of systems with an overhead that scales linearly with the system size, while for the AKLT model the overhead is polynomial. In all cases our approach shows some robustness against experimental imperfections.

Figure 1

Pictorial representation of the AKLT state. There are two virtual qubits (blue dots) at each site. Dots connected by an edge represent singlet states $|{\psi }^{-}⟩$ and ellipses refer to projections onto the three-dimensional triplet subspace, where one makes the following identification: $|\tilde{0}⟩=|00⟩$, $|\tilde{1}⟩=|11⟩$, $|\tilde{2}⟩=|{\psi }^{+}⟩=(1/\sqrt{2})(|01⟩+|10⟩)$.

Figure 2

(a) Plot of the maximal number of parties for which one can certify entanglement as a function of the noise $1-p$. (b) Similar plot for larger, experimentally better accessible values of $1-p$.