Optical Implementation of 2 × 2 Universal Unitary Matrix Transformations

Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization classical and quantum information processing. The ability implementing any n-dimensional unitary signal transformation by using reconfigurable optical hardware has recently led to pioneering concept programmable processor, whose basic building block (BB) must be correctly designed guarantee whole system is able perform n × universal (i.e., arbitrary) matrix transformations. Here, it demonstrated present architectures BB do not fulfil property (at least) in 2 processors, limiting number may generated. Aiming solve this fundamental constraint, theoretical tools required analyze design circuits their corresponding BBs presented. consequences mathematical framework explored, obtaining simple route implement different architectures, all them guaranteeing true functionality resulting processors. These findings pave way revisit high-dimensional unleashing potential integrated photonics technology.