James P. Crutchfield and Karoline Wiesner |
ABSTRACT: 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 provide closed-form expressions for a broad class of finitary quantum processes, noting when closed-form expressions cannot be given.