Geometric Measure: Multipartite Entanglement

Gerardo A. Paz-Silva, John Henry Reina

Songbo Xie

Massimo Blasone A, Fabio Dell’Anno, Silvio De Siena +2 more

We investigate the behaviour of multipartite entanglement in finite-size quantum spin systems, resorting to a hierarchy of geometric measures of multipartite entanglement recently introduced in the literature. In particular, we investigate the ground-state entanglement in the XY model defined on finite chains of N sites with periodic boundary conditions. We analyse the behaviour of the geometric measures of (N 1)-partite and (N/2)-partite entanglement and compare them with the Wei‐Goldbart geometric measure of global entanglement.

Debasis Sadhukhan, Sudipto Singha Roy, Amit Kumar Pal +3 more

Multiparty quantum states are useful for a variety of quantum information and computation protocols. We define a multiparty entanglement measure based on local measurements on a multiparty quantum state and an entanglement measure averaged on the postmeasurement ensemble. Using the generalized geometric measure as the measure of multipartite entanglement for the ensemble, we demonstrate, in the case of several well-known classes of multipartite pure states, that the localized multipartite entanglement can exceed the entanglement present in the original state. We also show that measurement over multiple parties may be beneficial in enhancing localizable multipartite entanglement. We point out that localizable generalized geometric measure faithfully signals quantum critical phenomena in well-known quantum spin models even when considerable finite-size effect is present in the system.

Ingemar Bengtsson, Karol Życzkowski

Massimo Blasone A, Fabio Dell’Anno, Silvio De Siena +2 more

We investigate the behavior of the multipartite entanglement in the finite size XY model by means of the hierarchical geometric measure of entanglement. By selecting specific components of the hierarchy, we study both global entanglement and genuinely multipartite entanglement.