Unitary operators are powerful tools in quantum information processing. For orbital angular momentum (OAM) domain, to achieve a unitary operation scheme with universality, scalability, and near-unity success probability simultaneously is still an open question regarding the reported schemes based on OAM parity sorters, spin-orbital coupling and multi-plane light conversion (MPLC) techniques. We have proposed and demonstrated a scalable and efficient scheme for programmable unitary operations in orbital angular momentum (OAM) domain. Based on matrix decomposition into diagonal and Fourier factors, arbitrary matrix operators can be implemented only by diagonal matrices alternately acting on OAM domain and azimuthal angle domain, which are linked by Fourier transform. Thus, the technical difficulties to implement arbitrary unitary operators could be significantly reduced. With numerical simulations, unitary matrices with dimensionality up to 6×6 are designed and discussed for OAM domain. As an alternative to verify our proposal, proof of principle experiments have been performed on path domain, in which an average fidelity of 0.97 is evaluated through 80 experimental results with dimensionality of 3×3. Furthermore, our proposal is also potential to provide a quantum operation protocol for other new photonic degrees of freedom (DOFs), if there exists the corresponding Fourier transform pair.

This work was published on National Science Open. Dr. Shikang Li is the first author and Professor Feng Xue is the corresponding author.