Published In

Physical Review A: Atomic, Molecular & Optical Physics

Document Type


Publication Date



Linear algebra, Schmidt coefficients, Schmidt rank


We prove that every unitary acting on any multipartite system and having operator Schmidt rank equal to 2 can be diagonalized by local unitaries. This then implies that every such multipartite unitary is locally equivalent to a controlled unitary with every party but one controlling a set of unitaries on the last party. We also prove that any bipartite unitary of Schmidt rank 2 is locally equivalent to a controlled unitary where either party can be chosen as the control, and at least one party can control with two terms, which implies that each such unitary can be implemented using local operations and classical communication (LOCC) and a maximally entangled state on two qubits. These results hold regardless of the dimensions of the systems on which the unitary acts.


This is the publisher's final PDF. Article appears in Physical Review A ( and is copyrighted by APS Journals (



Persistent Identifier

Included in

Physics Commons