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We prove that if any error channel has a Kraus decomposition that issimultaneously correctable and Hilbert-Schmidt (HS) complete, then theexistence of Kraus sets with these properties guarantees the correctability ofall 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.

Random-Unitary Depolarization Ensures the Correctability of All Quantum Channels