Finding quantum noiseless subsystems:
A linear-algebraic approach
We propose linear algebraic techniques for finding maximum dimensional noiseless subspaces and pure subsystems for a given quantum dynamical model. Noiseless subsystem are the most general structure that support protected realization of quantum information. After recalling the relevant characterization, we develop simple strategies to tackle particular cases and we sketch a possible approach for the general one. The linear algebraic problem is that of choosing a suitable basis in a finite dimensional Hilbert space, such that the relevant operators attain the desired block-form.