The structure of preserved information in quantum processes

We present a general operational framework for characterizing the types of information that can be preserved by a quantum process. We demonstrate that \emph{information preserving structures} (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- are isometric to fixed points of unital quantum processes. This implies that every IPS is a matrix algebra. A structure theorem for fixed points of an arbitrary process further provides a simple and efficient algorithm for finding all noiseless and unitarily noiseless IPS for any quantum process. This framework can be extended to study the structure of approximately preserved information.