Differential Geometry of Quantum States, Observables and Evolution

The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.Comment: 20 pages, comments are welcome

On the notion of composite system

The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.Comment: 9 pages. Comments are welcom

Focus point: classical and quantum information geometry

The interplay between Differential Geometry, Mathematical Statistics, Probability Theory and Quantum Mechanics resulting in the so-called field of Classical and Quantum Information Geometry represents one of the most effective examples of cross-fertilizations of modern Science. Roughly speaking, Information Geometry deals with the understanding of the differential geometric properties of suitable manifolds of Classical probability distributions and Quantum states, and with the concrete possible applications that such a theoretical understanding necessarily triggers