Information and Complementarity in a Proposed Which-path Experiment Using Photons

We propose a scheme to realize the famous two-slit gedanken experiment using photons. Measurements using optical parametric amplifiers (OPAs) are proposed to infer the probabilities that the input photon has taken a particular path in a Mach-Zehnder interferometer, without destroying the photon. Using information theory and Bayes' theorem, we find that the visibility of ensemble averaged interference fringes is inversely related to the which-path information that is made available by the OPAs. This is in agreement with the complementarity principle. A method is found to erase partially the which-path information before it is recorded; then by making conditional measurements the fringe visibility can be partially restored.