Figure 2

Single-photon controlled gates. (a) The quantum-circuit representation of a controlled gate CU, where the upper line represents a d-dimensional OAM qudit and the lower line represents an n-dimensional path qudit. (b) The schematics of an actual experimental setup for (a) where individual horizontal lines amount to real propagation paths. The scheme relies on the eigendecomposition of the unitary U as explained in the main text. In each path as many as d different OAM eigenstates can propagate simultaneously. (c) The folded version of (b) reduces the number of optical elements at the cost of using polarization as an additional degree of freedom. A photon enters in the horizontal polarization from the left and leaves the setup in the vertical polarization at the bottom. (d) The schematics of the controlled gate where the control qudit is played by the path modes and individual gates \(U^{k}\) act on OAM