Characterizing entanglement from correlations: the multi-partite case

In this talk we will discuss how entanglement is defined with respect to separability, and how the strategies for quantifying two-party entanglement can be extended to multiple parties. Though residual entanglement (i.e., what is left when two-party entanglement is subtracted away) is a popular concept for measuring three-party entanglement, we criticize this and expand on a new resource-based measure known as the tri-partite entanglement of formation. Though there remain multiple fundamental questions to be answered on measures of multi-partite entanglement, we show how the tri-partite entanglement of formation can be bounded from below using experimental correlations in much the same way as was done for two parties. Moreover, we give examples showing how much tripartite entanglement may be present in entangled photon triplets generated in nonlinear optics, and provide a general witness for N-partite entanglement. In our development of the N-partite witness, we also discovered something interesting about the nature of quantum correlations. Though there is no quantum-imposed limit to the correlations two parties can share (e.g., in both position and in momentum), there is such a limit for three or more parties.