**Realization of arbitrary discrete unitary transformations using spatial and internal modes of light** - Ish Dhand

Any lossless transformation on ns spatial and np internal modes of light can be described by an ns np × ns np unitary matrix, but no procedure to effect arbitrary ns np × ns np unitary matrix on the combined spatial and internal modes is known. We devise an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. Our realization uses beamsplitters and operations on internal modes to effect arbitrary linear transformations. The number of beamsplitters required to realize a unitary transformation is reduced as compared to existing realization by a factor equal to the dimension of the employed internal degree of freedom. Our algorithm thus enables the optical implementation of higher dimensional unitary transformations. (Based on arXiv:1508.06259)