Quantum Information Theory

How many (classical or quantum) bits would we need in order to store information from a given source? How much information could we reliably transmit via a noisy communication channel? What are the minimal resources necessary to transform one form of information into another? These are the key questions that information theory, classical or quantum, addresses. In essence, it is concerned with identifying and quantifying fundamental resources—but not specific methods, such as algorithms, or equipment—for generating, storing, manipulating, and transmitting the information. Information refers to the state of a physical system, and as Landauer (1991) uttered, it is physical. As such, the answers to the above questions must be different depending on the underlying physical principles. Quantum information theory is concerned with quantum mechanics. This new principle enriches classical information theory that is based on classical mechanics, bringing about fresh possibilities.

This collection of tutorial documents starts by introducing the notion of entropy, first classical and then quantum entropies. The entropy quantifies information and is the most fundamental concept in information theory. The collection next discusses quantum entanglement as a physical resource. As mentioned above, quantum information theory is far richer than its classical counterpart. Among many fundamental and technical differences, quantum entanglement makes the most striking one, as an intriguing resource that is not available in classical information. Not surprisingly, quantum entanglement forms the vast majority of topics studied in quantum information theory.

This collection aims to be a quick introduction to quantum information theory. It surveys only the most basic notions and ideas of quantum information theory. Unlike more traditional disciplines of physics, quantum information theory could look rather disordered or disoriented, especially when encountered at first, full of seemingly unrelated subjects. Once accustomed to the basic ideas and concepts introduced in this chapter, one can delve deeper into various advanced subjects by resorting to other more specialized texts including Chapters 11 and 12 of Nielsen & Chuang (2011).

See also Chapter 7 of the