Quantum dynamical entropy and decoherence rate

Quantum dynamical entropy and decoherence rate

We investigate quantum dynamical systems defined on a finite-dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann entropy, averaged over an ensemble of random pure states, is proved to be bounded from above by the partial entropy used to define the ALF-dynamical entropy. The...

Quantum Dynamical Semigroups and Decoherence

Quantum Chaos, Dynamical Stability and Decoherence

Giulio Casati1,2,3 and Tomaž Prosen4 1 Center for Nonlinear and Complex Systems, Universita’ degli Studi dell’Insubria, 22100 Como, Italy 2 Istituto Nazionale per la Fisica della Materia, unita’ di Como, 22100 Como, Italy, 3 Istituto Nazionale di Fisica Nucleare, sezione di Milano, 20133 Milano, Italy, 4 Department of Physics, Faculty of mathematics and physics, University of Ljubljana, 1000 Lj...

Quantum Dynamical Entropy from Relative entropy

In this exposition we prove an existence theorem for a quantum mechanical dynamical entropy based on von-Neumann’s measurement theory. To that end we introduced a Shannon type of information associated with a quantum channel or measurement based on Araki’s relative entropy. This is an invariance for the dynamics which generalizes Kolmogorov-Sinai ’s notion of dynamical entropy of a measure pres...

Decoherence and the rate of entropy production in chaotic quantum systems

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength). For longer times (but before equilibration)...