Foundations of Quantum Mechanics and Quantum Information Theory

In this chapter, we introduce the general theory of QM with two formulations. The first one is based on the Postulates (Axioms) of QM, which rather follows a traditional view, while the second one is devised for an application of quantum information science in a way to clarify the most general classes of quantum states, measurements, and time evolutions of a given quantum system under the possible presence of environment. By specifying the underling preconditions, we carefully explain their logical and physical connections between superficially different formulations.