# Differential Geometry of Quantum States, Observables and Evolution

## TL;DR

This paper reviews the geometrical approach to Quantum Mechanics, analyzing states, observables, and evolution through geometric structures, with a detailed discussion of the qubit example as an alternative to standard formulations.

## Contribution

It introduces a comprehensive geometric framework for quantum states and observables, offering new insights into their algebraic and structural properties.

## Key findings

- Geometrical structures underpin quantum states and observables.
- The geometric approach provides an alternative perspective to standard quantum mechanics.
- Qubit analysis illustrates the application of geometric methods.

## Abstract

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.