  We analyze how measured quantum dynamical systems store and process
information, introducing sofic quantum dynamical systems. Using recently
introduced information-theoretic measures for quantum processes, we quantify
their information storage and processing in terms of entropy rate and excess
entropy, giving closed-form expressions where possible. To illustrate the
impact of measurement on information storage in quantum processes, we analyze
two spin-1 sofic quantum systems that differ only in how they are measured.
