QMATH Lecture: Asymptotic entanglement concentration of W states

Speaker: Alonso Botero, University of South Carolina, Columbia

Title: Asymptotic entanglement concentration of W states

Abstract:
While the general problem of multipartite entanglement concentration remains open, one can still show that for certain classes of multipartite states, it is possible to asymptotically concentrate the entanglement of n copies of the state into a single canonical “totally entangled” state, i.e., with maximally mixed one-particle density matrices, between local Hilbert spaces of high dimension. In this talk we show how this happens for one such class of states, the three-qubit W class, which admits a concentration protocol akin to the distortion-free protocol of Hayashi and Matsumoto. In particular, we show how this remarkable property of W states follows from a multi-local Schur transform, permutation symmetry, and the algebra of SLOCC covaraints for three-qubit states. If time permits, we will also discuss how the asymptotic tail exponents can be computed in principle, and discuss some partial results in this respect.