  The Anderson localization transition is one of the most well studied examples
of a zero temperature quantum phase transition. On the other hand, many open
questions remain about the phenomenology of disordered systems driven far out
of equilibrium. Here we study the localization transition in the prototypical
three-dimensional, noninteracting Anderson model when the system is driven at
its boundaries to induce a current carrying non-equilibrium steady state.
Recently we showed that the diffusive phase of this model exhibits extensive
mutual information of its non-equilibrium steady-state density matrix. We show
that that this extensive scaling persists in the entanglement and at the
localization critical point, before crossing over to a short-range (area-law)
scaling in the localized phase. We introduce an entanglement witness for
fermionic states that we name the mutual coherence, which, for fermionic
Gaussian states, is also a lower bound on the mutual information. Through a
combination of analytical arguments and numerics, we determine the finite-size
scaling of the mutual coherence across the transition. These results further
develop the notion of entanglement phase transitions in open systems, with
direct implications for driven many-body localized systems, as well as
experimental studies of driven-disordered systems.
