We prepared polarization-entangled photon pairs and sent one of the photons through a Mach-Zehnder interferometer. The apparatus was arranged so that when going through each arm of the interferometer the pairs were in a different Bell state. The distinguishability of the interferometer paths was determined by projecting the entangled state of the two photons with a polarizer placed in the path of the photon that does not go through the interferometer. As a consequence, actions on the remote photon determined nonlocally the visibility of the interference pattern. We present a full theoretical analysis and experimental results that confirm the theoretical predictions. © 2005 The American Physical Society.