Double-Fock superposition interferometry for differential diagnosis of decoherence

Interferometric signals are degraded by decoherence, which encompasses dephasing, mixing and any distinguishing which-path information. These three paradigmatic processes are fundamentally different, but, for coherent, single-photon and N00N-states, they degrade interferometric visibility in the very same way, which impedes the diagnosis of the cause for reduced visibility in a single experiment. We introduce a versatile formalism for many-boson interferometry based on double-sided Feynman diagrams, which we apply to a protocol for differential decoherence diagnosis: twin-Fock states vertical bar N, N > with N >= 2 reveal to what extent decoherence is due to path distinguishability or to mixing, while double-Fock superpositions vertical bar N: M > = (vertical bar N, M > + vertical bar M, N >)/root 2 with N > M > 0 additionally witness the degree of dephasing. Hence, double-Fock superposition interferometry permits the differential diagnosis of decoherence processes in a single experiment, indispensable for the assessment of interferometers.