Lecture Notes

"Quantum Information Theory for Engineers: an Interpretative Approach"

can be downloaded from

It comprise lectures on quantum computing and quantum information theory that I taught during the last ten years for students of electrical engineering, mathematics, and computer science. These notes present an alternative entrance to quantum information theory that is suitable for students studying engineering, but perhaps also for people interested in physics and philosophy of physics.

A supplement to these notes can be found in Free Climbing through Physics and Probability.

Historically, C.F. von Weizsäcker might be considered as the father of quantum information theory. In the 1950ies he started on the basis of quantum information theory to describe the physical conceptions of space-time, particles, and relativistic quantum fields. In his books, "Aufbau der Physik", "Zeit und Wissen", and "The Structure of Physics" (see the references in my lecture notes), he showed how to construct these physical concepts from qubits. In particular, he tried to provide a unified description of nature solely on the basis of quantum information theory.

He used the name "ur" instead of "qubit", and called his theory ur theory. The name qubit was introduced much later in 1995, and is attributed to Benjamin Schumacher. An ur or qubit is represented by a vector in a two-dimensional complex Hilbert space with the universal symmetry group SU(2), and can be characterized as one bit of potential information. Frequently, physicists speak of spinors instead of urs or qubits.

The ur theory can be viewed as the start of quantum theory of information, where spinorial symmetry groups are considered to give rise to the structure of space and time. Finkelstein, Penrose, and von Weizsäcker are the leading spinorists in science.

C.F. von Weizsäcker tried to realize the Kantian idea of justifying the fundamental laws of nature from our experience with binary alternatives. His point of view is essentially based on a probability theory within a temporal logic and the concept of alternatives. In particular, empirical predictions can be reduced to qubits. They permit a decomposition of state spaces into the tensor product of two-dimensional complex Hilbert spaces.

In addition, his ur theory allows a completely new perspective on the three entities matter, energy, and gravitation. Werner Heisenberg wrote about his concept "that the realization of von Weizsäcker's program requires thinking at such a high degree of abstraction that up to now – at least in physics – has never happened." Not surprisingly, Weizsäcker's approach was hardly appreciated, perhaps it was far too abstract. Moreover, his predictions were beyond the imagination of most physicists. For instance, that one proton is made up of 10^40 qubits, is hard to believe, even today. However, a quantum field theory, particles, and a cosmological model are presented in von Weizsäcker's framework. His work is hardly mentioned in the literature. For example, the well-known Stanford Encyclopedia of Philosophy does not even mention his name under the keywords "Quantum Entanglement and Information" as well as "Quantum Logic and Probability Theory", although this Encyclopedia covers the topics in great detail with an elaborate bibliography.

My lecture notes are influenced and related in some parts on the ur theory. Due to the abstractness of von Weizsäcker's approach and the resulting mathematical difficulties, however, for an engineer his books are hard to read. Hence, my notes differ from ur theory in notation, representation, contents, but also in several used concepts. I will write a supplement to my lecture notes that presents the basic ideas of the ur theory, perhaps, written more suitable for engineers. This supplement will be based on my lecture notes, but will be presented in a less abstract form.