  We demonstrate a fully-tunable multi-state Fano system in which
remotely-implemented quantum states interfere with each other through their
coupling to a mutual continuum. On tuning these resonances near coincidence a
robust avoided crossing is observed, with a distinctive character that confirms
the continuum as the source of the coupling. While the continuum often serves
as a source of decoherence, our work therefore shows how its presence can
instead also be essential to mediate the interaction of quantum states, a
result that could allow new approaches to engineer the collective states of
nanostructures.
