SYMBOLIC DYNAMICS OF SUCCESSIVE QUANTUM-MECHANICAL MEASUREMENTS

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 Renyi entropies K(beta) with the help of the transfer-matrix method. A nontrivial dependence on beta is observed. We show that the Renyi 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.