Quantum dynamical entropy and decoherence rate

Abstract

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 rate of decoherence induced by the sequence of the von Neumann projectors measurements is shown to be maximal, if the measurements are performed in a randomly chosen basis. The numerically observed linear increase of entropies is attributed to free-independence of the measured observable and the unitary dynamical map.

13 pages, 3 figures

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• Scalable Noise Estimation with Random Unitary Operators
• Bridging entanglement dynamics and chaos in semiclassical systems
• Superdensity Operators for Spacetime Quantum Mechanics
• Quantum Variance and Ergodicity for the baker's map
• Entanglement entropy converges to classical entropy around periodic orbits
• Universality of spectra for interacting quantum chaotic systems
• A semiclassical condition for chaos based on Pesin theorem
• Quantum Chaos and Quantum Randomness - Paradigms of Entropy Production on the Smallest Scales
• Quantum Entropies and Decoherence for the Multiparticle Quantum Arnol'd Cat
• Linear dynamical entropy and free-independence for quantized maps on the torus
• Symmetry Properties of Quantum Dynamical Entropy
• Orders of chaoticity of unitaries
• Determination of the noise parameters in a one-dimensional open quantum system
• Diagnosing chaos with projected ensembles of process tensors
• Behavior of correlation functions in the dynamics of the Multiparticle Quantum Arnol'd Cat