Schematic representation of a three-path interferometer with path indicators. The status of the path indicators changes when a photon passes through them. BS1 is short for a three-port beam splitter and BS2 is a nine-port beam splitter. The light paths are labeled as 0, 1, 2 after BS1, and the nine light paths are labeled as path ab (a ϵ {0,1,2} and b ϵ {α,β, ϒ}) after the path indicators. The degree of freedom {α,β, ϒ} will be traced out when we collect the experimental data, therefore only three paths are displayed after the path indicators.