Random-Unitary Depolarization Ensures the Correctability of All Quantum Channels

Abstract: We prove that if any error channel has a Kraus decomposition that is simultaneously correctable and Hilbert-Schmidt (HS) complete, then the existence of Kraus sets with these properties guarantees the correctability of all quantum channels. As a proof of the existence of such Kraus sets, the $n$-level depolarization channel is shown to have a random-unitary (RU) decomposition that is both HS complete and correctable due its RU nature, thereby proving that all quantum channels are correctable. As an application, conditions for universal error-correction operations are presented.