Paradoxical behavior in a triple cascade of Mach–Zehnder interferometers
Allen Parks, Scott E. Spence · Journal of Physics A Mathematical and Theoretical · 2012
A gedanken experiment is considered using a cascade of three Mach–Zehnder interferometers (MZIs). The first MZI in the cascade is used to judiciously prepare the pre-selected state of a single photon launched into one of its input ports and the third MZI in the cascade is used to judiciously prepare the post-selected state of the photon emerging from one of its output ports. Paradoxical behavior arises when a weak measurement of photon occupation number is independently performed along each of the two paths emerging from the first MZI’s output ports, i.e., the pointer associated with the weak measurement along one path registers a large positive occupation number and that for the weak measurement along the other path registers a large negative occupation number. Although each of these measurements contradicts the fact that there is only one photon in the interferometer, quantum mechanics resolves this paradox in an interesting way by ensuring that the sum of these occupation numbers is always 1.