Compactifying linear optical unitaries using multiport beamsplitters

Abstract: We show that any $N$-dimensional unitary matrix can be realized using a finite sequence of concatenated identical multiport beamsplitters. Our construction is based on a Lie group theorem and is explicitly demonstrated for the two- and three-dimensional cases. We further establish that the widely used Clements decomposition naturally arises as a special case of this general framework. As an application, we present a reconfigurable linear optical circuit that implements a three-dimensional unitary emerging in the unambiguous discrimination of two nonorthogonal qubit states.