Phase-Subtractive Interference and Noise-Resistant Quantum Imaging with Two Undetected Photons

We present a quantum interference phenomenon in which four-photon quantum states generated by two independent sources are used to create a two-photon interference pattern without detecting two of the photons. Contrary to the common perception, the interference pattern can be made fully independent of phases acquired by the photons detected to construct it. However, it still contains information about spatially dependent phases acquired by the two undetected photons. This phenomenon can also be observed with fermionic particles. We show that the phenomenon can be applied to develop an interferometric, quantum phase imaging technique that is immune to uncontrollable phase fluctuations in the interferometer and allows image acquisition without detecting the photons illuminating the object.