A reminder of open systems, decoherence and quantum information

The first lesson, covering the first chapter, began by returning to the essential results of previous years, in particular the description of open quantum systems. Quantum information systems are always interacting with an environment, which plays an essential role in their manipulation and measurement. Open systems are described using the density operator formalism, which replaces the state vector (or wave function) formalism of elementary quantum mechanics. We have recalled this formalism by summarizing the properties of the density operator of an open system. We also recalled the universal properties of transformations of the system's density operator. We reviewed the different types of measurement possible (projective and generalized measurements) and the methods of continuous observation of a single quantum system (observation of quantum jumps simulated by the so-called quantum Monte Carlo method). The first chapter concluded with a brief review of quantum information, the definition of quantum bits and elementary one- and two-qubit gates, and the generation of intricate Schrödinger cat states in qubit systems subjected to the action of single gates. The fragility of these states was highlighted.