Multi-distributed Entanglement in Finitely Correlated Chains

Abstract

The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of their finitely correlated structure. These states are recursively constructed by means of an auxiliary density matrix ρon a matrix algebra B and a completely positive map E: A \otimes B -> B, where A is the spin 2\times 2 matrix algebra. General structural results for the infinite chain are therefore obtained by explicit calculations in (finite) matrix algebras. In particular, we study not only the entanglement shared by nearest-neighbours, but also, differently from previous works, the entanglement shared between connected regions of the spin-chain. This range of possible applications is illustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement of connected regions can actually be reached.

7 pages, 2 figures, to be published in Eur.Phys.Lett