  We propose a class of path-entangled photon Fock states for robust quantum
optical metrology, imaging, and sensing in the presence of loss. We model
propagation loss with beam-splitters and derive a reduced density matrix
formalism from which we examine how photon loss affects coherence. It is shown
that particular entangled number states, which contain a special superposition
of photons in both arms of a Mach-Zehnder interferometer, are resilient to
environmental decoherence. We demonstrate an order of magnitude greater
visibility with loss, than possible with N00N states. We also show that the
effectiveness of a detection scheme is related to super-resolution visibility.
