Efficient Device-Independent Entanglement Detection for Multipartite Systems

Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite states continues to be a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of particles or require more information on the state than what is attainable in everyday experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, it scales efficiently with the number of particles, thus allowing for application to systems composed by up to few tens of particles. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.

Popular Summary

Entanglement is a set of correlations observed among quantum particles that does not have a classical analog. It is also a key feature for several quantum information protocols. Detecting its presence in systems with many particles, however, remains experimentally and theoretically challenging. The first barrier is the exponential amount of information required to reconstruct the system’s state. The second is that, even if the quantum state is known, the available methods are computationally too demanding even for systems composed of few particles. We introduce a technique for entanglement detection that is both computationally and experimentally efficient.

Our method, which relies on the detection of nonlocality, involves a number of experimental configurations that grow only polynomially with the size of the system, which makes it applicable to states of up to a few tens of particles. Moreover, it is based on the knowledge of few-body correlators, making it amenable to practical implementation. Lastly, our method is device independent, meaning that it allows one to assess entanglement without assuming any prior knowledge of the prepared state or the measurements performed.

We expect that our findings can contribute to advancing the field of entanglement detection towards larger systems. In particular, our approach can supersede the current methods used to detect entanglement in state-of-the-art experiments involving tens of particles.

Figure 1

Pictorial representation of the sets of correlations, together with our approach to detection of multipartite nonlocality. The $\mathcal{L}$ and $\mathcal{Q}$ sets delimit the local and quantum correlations, respectively. As shown here, the first forms a polytope, namely, a convex set delimited by a finite amount of extremal points, while the second, despite still being convex, is not a polytope. The light orange sets are the first representatives of the hierarchy ${\mathcal{L}}_1\supseteq {\mathcal{L}}_2\supseteq \cdots \supseteq \mathcal{L}$ approximating the local set from outside. It can be seen that some of the quantum correlations lie outside the ${\mathcal{L}}_2$, meaning that they are detected as nonlocal from the SDP relaxation at the second level. The dotted line shows a Bell-like inequality that can be obtained by the corresponding dual problem.

Figure 2

Representatives of the graphs associated to the classes of states that have been studied with the SDP method: (a) linear graph states, (b) loop graph states, (c) 2D cluster states.