Coauthors: Man-Duen Choi and David Kribs

Quantum error correction deals with correcting errors introduced via quantum channels, modelled by trace-preserving completely positive maps. Correctable codes are subsystems of the overlying Hilbert space on which the channel has a left inverse. Given a unital completely positive map, the multiplicative domain of that map is the largest subalgebra on which the map acts as a *-homomorphism. We show that for a unital quantum channel, the codes that are correctable via conjugation by a unitary (called unitarily correctable subsystems) are exactly that map's multiplicative domain. We also show that if we remove the requirement that the map be unital, a weaker relationship between the two notions still holds. Furthermore, a generalization of the multiplicative domain can be defined that captures all correctable codes for arbitrary channels.