Characterizing multipartite entanglement without shared reference frames

Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension, we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore, we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.

Figure 1

Here we illustrate the noise resistance of the entanglement detection criterion derived from Eq. (10). For a value of $p>\sqrt{\frac{2}{5}}$, the three-dimensional generalized GHZ state mixed with white noise is detected to be entangled, and for $p>\sqrt{\frac{4}{5}}$ it is detected to be genuinely multipartite entangled. Compared to the noise resistance of witnesses directly tailored towards detecting exactly this state, the exhibited noise resistance is of course rather weak (e.g., compared to $p>\frac{1}{4}$ from Ref. [6]), which is the price to be paid for local unitary invariance. On the other hand, the witnesses designed to detect exactly this state would inevitably fail if the state undergoes a local unitary rotation in just one of the subsystems.