  We introduce ways to measure information storage in quantum systems, using a
recently introduced computation-theoretic model that accounts for measurement
effects. The first, the quantum excess entropy, quantifies the shared
information between a quantum process's past and its future. The second, the
quantum transient information, determines the difficulty with which an observer
comes to know the internal state of a quantum process through measurements. We
contrast these with von Neumann entropy and quantum entropy rate and provide a
closed-form expression for the latter for the class of deterministic quantum
processes.
