Entanglement-induced invariance in bilinear interactions

We point out a symmetry exhibited by pairs of entangled states and discuss its possible applications in quantum information. More specifically, we consider quadripartite systems prepared in bipartite product states of the form vertical bar Psi > = vertical bar psi >(12) circle times vertical bar psi >(34) and let the uncorrelated subsystems 14 and 23 interact by a given unitary U-14 circle times U-23 describing two bilinear interactions: we show that entanglement between the noninteracting subsystems 12 and 34 may lead to invariance of vertical bar Psi > under the action of the unitary, i.e., make vertical bar Psi > an eigenstate of U-14 circle times U-23. We call this phenomenon entanglement induced transparency and investigate its occurrence both in continuous variable and qubit systems. We also discuss its possible applications to bath engineering, double swapping and remote inversion.