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Preserved information in quantum processes

David Poulin, California Institute of Technology

(Session 12 : Sunday from 10:45-11:15)

Abstract. I will derive a general structure theorem characterizing the information that can be preserved by a quantum process (CPTP map). This characterization builds on a very simple yet powerful operational definition of the notion of being preserved: a set of quantum states is preserved by a process if the states are as distinguishable before and after the process. This definition encompasses noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes. More generally, I will demonstrate that all such information-preserving structure (IPS) is isomorphic to a matrix algebra. This provides a simple and efficient algorithm for finding all noiseless and unitarily noiseless IPS.