Coexistence of full which-path information and interference in Wheelerʹs delayed-choice experiment with photons

We present a computer simulation model that is a one-to-one copy of an experimental realization of Wheelerʹs delayed-choice experiment that employs a single photon source and a Mach–Zehnder interferometer composed of a 50/50 input beam splitter and a variable output beam splitter with adjustable reflection coefficient R [V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, J.-F. Roch, Phys. Rev. Lett. 100 (2008) 220402]. For 0⩽R⩽0.5, experimentally measured values of the interference visibility V and the path distinguishability D, a parameter quantifying the which-path information (WPI), are found to fulfill the complementary relation V2+D2⩽1, thereby allowing to obtain partial WPI while keeping interference with limited visibility. The simulation model that is solely based on experimental facts that satisfies Einsteinʹs criterion of local causality and that does not rely on any concept of quantum theory or of probability theory, reproduces quantitatively the averages calculated from quantum theory. Our results prove that it is possible to give a particle-only description of the experiment, that one can have full WPI even if D=0, V=1 and therefore that the relation V2+D2⩽1 cannot be regarded as quantifying the notion of complementarity.