  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.
