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script Quantum Information Theory by Renato Renner
1 Introduction
The very process of doing physics is to acquire information about the world around us.
At the same time, the storage and processing of information is necessarily a physical
process. It is thus not surprising that physics and the theory of information are inherently
connected.1 Quantum information theory is an interdisciplinary research area whose goal
is to explore this connection.
As the name indicates, the information carriers in quantum information theory are
quantummechanical systems (e.g., the spin of a single electron). This is in contrast to
classical information theory where information is assumed to be represented by systems
that are accurately characterized by the laws of classical mechanics and electrodynamics
(e.g., a classical computer, or simply a piece of paper). Because any such classical system
can in principle be described in the language of quantum mechanics, classical information
theory is a (practically significant) special case of quantum information theory.
The course starts with a quick introduction to classical probability and information theory.
Many of the relevant concepts, e.g., the notion of entropy as a measure of uncertainty,
can already be defined in the purely classical case. I thus consider this classical part as a
good preparation as well as a source of intuition for the more general quantummechanical
treatment.
We will then move on to the quantum setting, where we will spend a considerable
amount of time to introduce a convenient framework for representing and manipulating
quantum states and quantum operations. This framework will be the prerequisite for
formulating and studying typical informationtheoretic problems such as information storage
and transmission (with possibly noisy devices). Furthermore, we will learn in what
sense information represented by quantum systems is different from information that is
represented classically. Finally, we will have a look at applications such as quantum key
distribution.
I would like to emphasize that it is not an intention of this course to give a complete
treatment of quantum information theory. Instead, the goal is to focus on certain key
concepts and to study them in more detail. For further reading, I recommend the standard
textbook by Nielsen and Chuang [6]. Also, I would like to mention the course on
quantum computation [11] by Stefan Wolf (Computer Science Department). Wolf’s course
is somewhat complementary in the sense that it focuses on quantum computation, while
this course is on quantum information.
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