Entanglement replication via quantum repeated interactions

We study entanglement creation between two independent XX chains, which are repeatedly coupled locally to spin-1/2 Bell pairs. We show analytically that in the steady state the entanglement of the Bell pairs is perfectly transferred to the chains, generating large-scale interchain pair correlations. However, before the steady state is reached, within a growing causal region around the interacting locus the chains are found in a current driven nonquilibrium steady state (NESS). In the NESS, the chains cross entanglement decays exponentially with respect to the distance to the boundary sites with a typical length scale which is inversely proportional to the driving current.