Compactifying linear optical unitaries using multiport beamsplitters

We show that any N-dimensional unitary matrix can be realized using a finite sequence of concatenated identical fixed multiport beamsplitters (MBSs) and phase shifters (PSs). Our construction is based on a Lie group theorem applied to existing decompositions. Using the Bell-Walmsley-Clements framework, we prove that any N-dimensional unitary requires N+2 phase masks, N-1 fixed MBSs, and N-1 BSs. Our scheme requires only O (N) fixed, identical components (MBSs and BSs) compared to the O (N²) fixed BSs required by conventional schemes (e. g. , Clements), all while keeping the same number of PSs. Experimentally, these MBS can be realized as a monolithic element via femtosecond laser writing, offering superior performance through reduced insertion losses. 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.