In Chapters 1 and 2 we developed the necessary mathematical apparatus and terminology that will be used throughout this book. Chapter 3 has provided some heuristics and gently led us to the threshold of quantum mechanics. It is now time to open the door, introduce the basic concepts and tools of the trade, and continue our journey to quantum computing.

In Section 4.1 we spend a few words on the motivations behind quantum mechanics. We then introduce quantum states and how they are distinguishable from one another through observations. Section 4.2 describes observable physical quantities within the quantum framework. How observable quantities are measured is the topic of Section 4.3. The dynamics of quantum systems, i.e., their evolution in time, is the focus of Section 4.4. Finally, in Section 4.5, we revisit the tensor product and show how it describes the way in which larger quantum systems are assembled from smaller ones. In the process, we meet the crucial notion of entanglement, a feature of the quantum world that pops up again in the chapters ahead.

QUANTUM STATES

Why quantum mechanics? To answer this question, we have to hearken back in time to the dawn of the twentieth century. Classical mechanics still dominated the scene, with its double-pronged approach: particles and waves.