Verification procedures for quantum noiseless subsystems
Lorenza Viola, Emanuel H. Knill · Physical Review A · 2003
We examine the problem of verifying the implementation of a desired noiseless subsystem from a quantum error-correcting perspective. General conditions are identified, under which the verification of error-correcting behavior against a linear set of errors $\mathcal{E}$ suffices for the verification of noiseless subsystems of an error algebra $\mathcal{A}$ contained in $\mathcal{E}.$ From a practical standpoint, our results imply that the verification of a noiseless subsystem need not require the explicit verification of noiseless behavior for all possible initial states of the syndrome subsystem.