Taming Multiparticle Entanglement

We present an approach to characterize genuine multiparticle entanglement by using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated by using semidefinite programing and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponential improvement compared with existing schemes.

Figure 1

For three qubits, there are three convex sets of states that are separable with respect to a fixed bipartition, namely, the bipartitions $A|BC$, $B|AC$, and $C|AB$ (blue, dashed lines). Their convex hull (thick blue, dashed line) is the set of biseparable states. Each of the three sets is contained within the set of states that are PPT with respect to the corresponding bipartition (red, solid lines). Their convex hull forms the set of PPT mixtures (thick red, solid line).