Lecture Notes

"Quantum Information Theory for Engineers: an Interpretative Approach"

can be downloaded from

It comprises 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 the philosophy of physics.

Historically, C.F. von Weizsäcker might be considered the father of quantum information theory. In the 1950s, 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). It 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 the quantum theory of information, in which 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 an entirely 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 to some parts of the ur theory. Due to the abstractness of von Weizsäcker's approach and the resulting mathematical difficulties, however, his books are hard to read for an engineer. Hence, my notes differ from ur theory in notation, representation, and contents, but also in several used concepts. Due to this abstractness, I have written a supplement to my lecture notes:

"A Unified treatment of classical probability, thermodynamics, and quantum information theory"

which can be downloaded from

https://doi.org/10.15480/882.3770

Chapter 6 presents the basic ideas of the ur theory and provides a brief description of the history of Weizsäcker's original theory.

Now, Weizsäcker's research is very relevant again. In 1990, Wheeler discussed in the paper "Information, Physics, Quantum: The Search for Links" the fundamental relationship between physics, quantum theory, and information. Section 19.2 has the title "It from Bit." It symbolizes the idea that every item of the physical world has an immaterial source and explanation at the bottom. What we call reality arises in the last analysis from posing yes-or-no questions.

In 2015, the article "It from Qubit: Simons Collaboration on Quantum Fields, Gravity, and Information" starts on page 1 with the statement:

When Shannon formulated his groundbreaking theory of information in 1948, he did not know what to call its central quantity, a measure of uncertainty. Von Neumann recognized Shannon's formula from statistical physics and suggested the name entropy. This was but the first in a series of remarkable connections between physics and information theory. Later, tantalizing hints from the study of quantum fields and gravity, such as the Bekenstein-Hawking formula for the entropy of a black hole, inspired Wheeler's famous 1990 exhortation to derive "it from bit", a three-syllable manifesto asserting that, to properly unify the geometry of general relativity with the indeterminacy of quantum mechanics, it would be necessary to inject fundamentally new ideas from information theory. Wheeler's vision was sound, but it came twenty-five years early. Only now is it coming to fruition, with the twist that classical bits have given way to the qubits of quantum information theory. Simons Collaboration

The members of Simon's collaboration include well-known leaders in quantum information and the fundamentals of physics, among them Aaronson, Aharonov, Hayden, Preskill, and Susskind.

Forgotten is Weizsäckers work who already dealt with these fundamental questions in probability, information, and physics in the fifties. Concerning Simon's statement that ''Wheeler's vision was sound, but it came twenty-five years early``, Weizsäcker's theory came sixty years early. He attempted to reconstruct physics with binary alternatives.

By the way, Wheeler was invited already in 1980 by Weizsäcker to the fourth conference on Ur Theory and consequences. Ten years later, Wheeler gave a lecture with the very intuitive title "It from Bit". However, Wheeler did not reference the existing research by Weizsäcker and his co-workers. It shows that some physicists don't like to quote.