Dynamics, Information and Complexity in Quantum Systems

This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts:

Part One: Classical Dynamical Systems

• Addresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity.
• Includes a survey of the theory of simple perceptrons and their storage capacity.

Part Two: Quantum Dynamical Systems

• Focuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems.
• Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum   systems with infinitely many degrees of freedom.
• Introduces a model ofquantum perceptron whose storage capacity is computed and compared with the classical one.

Part Three: Quantum Dynamical Entropies and Complexities

• Devoted to quantum dynamical entropies and algorithmic complexities.

This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.

Introduction.- Classical Dynamics and Ergodic Theory.- Dynamical Entropy and Information.- Algorithmic Complexity.- Machine Learning.- Quantum Mechanics of Finite Degrees of Freedom.- Quantum Information Theory.- Quantum Mechanics of Infinite Degrees of Freedom.- Quantum Dynamical Entropies.- Quantum Algorithmic Complexities.- Quantum Machine Learning.

Fabio Benatti is an Associate Professor of the Department of Physics at the University of Trieste, Italy. He received the degree in Physics from the University of Trieste and the PhD in Mathematical Physics from SISSA – the International School for Advanced Studies in Trieste. He was post-doctoral fellow at the Institute for Theoretical Physics of the University of Vienna and at the Dublin Institute for Advanced Studies. His research interests include open quantum systems, quantum many-body physics, quantum information and quantum entropies. Also, Prof. Benatti is keen on exploring algorithmic complexity issues at the interface between classical and quantum behaviors.