  We address a fundamental question of quantum optics: Can a beam of light
mediate coherent Hamiltonian interactions between two distant quantum systems?
This is an intriguing question whose answer is not a priori clear, since the
light carries away information about the systems and might be subject to
losses, giving rise to intrinsic decoherence channels associated with the
coupling. Our answer is affirmative and we derive a particularly simple
sufficient condition for the interactions to be Hamiltonian: The light field
needs to interact twice with the systems and the second interaction has to be
the time reversal of the first. We demonstrate that, even in the presence of
significant optical loss, coherent interactions can be realized and generate
substantial amounts of entanglement between the systems. Our method is directly
applicable for building hybrid quantum systems, with relevant applications in
the fields of optomechanics and atomic ensembles.
