Experimental realization of any discrete unitary operator

TLDR

Optical experiments can be performed with any type of radiation, such as photons or atoms. A recursive algorithm decomposes any N×N unitary into a sequence of two‑dimensional beam‑splitter operations, which are implemented with optical devices to enable measurement of any discrete Hermitian observable. The study demonstrates that any finite‑dimensional unitary operator can be realized experimentally with optical devices, making higher‑dimensional discrete quantum systems accessible.

Abstract

An algorithmic proof that any discrete finite-dimensional unitary operator can be constructed in the laboratory using optical devices is given. Our recursive algorithm factorizes any N\ifmmode\times\else\texttimes\fi{}N unitary matrix into a sequence of two-dimensional beam splitter transformations. The experiment is built from the corresponding devices. This also permits the measurement of the observable corresponding to any discrete Hermitian matrix. Thus optical experiments with any type of radiation (photons, atoms, etc.) exploring higher-dimensional discrete quantum systems become feasible.