Entangled Fock states for robust quantum optical metrology, imaging, and sensing

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 path-entangled parallel to N,0 >+parallel to 0,N > states. We also show that the effectiveness of a detection scheme is related to super-resolution visibility.