We consider successive measurements on quantum-mechnical systems and investigate the way in which sequences of measurements produce information. The eigenvalues of suitable projection operators form symbolic sequences that characterize the quantum system under consideration. For several model systems with finite-dimensional state space, we explicitly calculate the probabilities to observe certain symbol sequences and determine the corresponding Rényi entropies K(β) with the help of the transfer-matrix method. A nontrivial dependence on β is observed. We show that the Rényi entropies as well as the symbol-sequence probabilities of the quantum-mechanical measurement process coincide with those of appropriate classes of one-dimensional chaotic maps.

• Received 27 May 1992

DOI:https://doi.org/10.1103/PhysRevA.46.6265