We provide a graphical description of multi-party entanglement based on a center-of-mass analogy. This description clarifies the existence of entanglement restrictions in the form of inequalities. Connections with optical polarization are discussed.
We provide a graphical description of the entanglement of pure-state multiparty systems based on an analogy between a bipartite purity analysis and the centroid of a collection of point masses. This description applies to quantum systems with N parties, each with an arbitrary number of (discrete) states. The case of N qubits is highlighted for simplicity. This geometric description illustrates some of the restrictions in the form of inequalities that apply to entanglement in multiparty systems.
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.
We present a general method to find the upper and lower bounds on the generalized entanglement of formation for multi-party systems. The upper and lower bounds can be expressed in terms of the bi-partite entanglements of formation and/or entropies of various subsystems. The examples for tri- and four-party systems in the both pure states and mixed states are given. We also suggest a little modified definition of generalized entanglement of formation for multi-party systems if EPR pairs are thought of belonging to the set of maximally entangled states.