Figure 4
Michelson interferometer configuration for Xd(p) gate. This is the folded version of the Mach-Zehnder setup in Fig. 3. The state \(|dp{\rangle }_{OAM}\) exits on spatial mode 0 and after a reflection on SPP(−pd) becomes \(\mathrm{|0}{\rangle }_{OAM}\). All other OAM states \(|jp{\rangle }_{OAM}\), \(j\ne d\), are left invariant by a double reflection on retro-reflectors R. Subsequently, all states re-enter the sorter from the opposite direction, thus performing \({S}_{d}^{-\mathrm{1/}p}\), and end up in the same spatial mode |0〉m. A circulator C separates the output from the input. Cases (a and b) are equivalent to Fig. 3(a,b), respectively.
