We cannot overstate the importance of Shannon's contribution to modern science. His introduction of the field of information theory and his solutions to its two main theorems demonstrate that his ideas on communication were far beyond the other prevailing ideas in this domain around 1948.

In this chapter, our aim is to discuss Shannon's two main contributions in a descriptive fashion. The goal of this high-level discussion is to build up the intuition for the problem domain of information theory and to understand the main concepts before we delve into the analogous quantum information-theoretic ideas. We avoid going into deep technical detail in this chapter, leaving such details for later chapters where we formally prove both classical and quantum Shannon-theoretic coding theorems. We do use some mathematics from probability theory, namely, the law of large numbers.

We will be delving into the technical details of this chapter's material in later chapters (specifically, Chapters 10, 12, and 13). Once you have reached later chapters that develop some more technical details, it might be helpful to turn back to this chapter to get an overall flavor for the motivation of the development.

Data Compression

We first discuss the problem of data compression. Those who are familiar with the Internet have used several popular data formats such as JPEG, MPEG, ZIP, GIF, etc. All of these file formats have corresponding algorithms for compressing the output of an information source.