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.

5 pages, 1 figure, 1 table; updated with corrections; http://cse.ucdavis.edu/~cmg/compmech/pubs/iqc.htm