Unambiguous path discrimination in a two-path interferometer

When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon ("signal") through a Mach--Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon ("idler") whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer \emph{cannot be known}; and every photon that emerges from the dark output port of the balanced interferometer has a \emph{known path}.