In Spring 2017, I taught a new undergraduate course at UT Austin, entitled Introduction to Quantum Information Science. There were about 60 students, mostly CS but also with strong representation from physics, math, and electrical engineering. One student, Ewin Tang, made a previous appearance on this blog. But today belongs to another student, Paulo Alves, who took it upon himself to make detailed notes of all of my lectures. Using Paulo’s notes as a starting point, and after a full year of procrastination and delays, I’m now happy to release the full lecture notes for the course. Among other things, I’ll be using these notes when I teach the course a second time, starting … holy smokes … this Wednesday.
I don’t pretend that these notes break any new ground. Even if we restrict to undergrad courses only (which rules out, e.g., Preskill’s legendary notes), there are already other great quantum information lecture notes available on the web, such as these from Berkeley (based on a course taught by, among others, my former adviser Umesh Vazirani and committee member Birgitta Whaley), and these from John Watrous in Waterloo. There are also dozens of books—including Mermin’s, which we used in this course. The only difference with these notes is that … well, they cover exactly the topics I’d cover, in exactly the order I’d cover them, and with exactly the stupid jokes and stories I’d tell in a given situation. So if you like my lecturing style, you’ll probably like these, and if not, not (but given that you’re here, there’s hopefully some bias toward the former).

To be published by Cambridge University Press in April 2018.

Upon publication this book will be available for purchase through Cambridge University Press and other standard distribution channels. Please see the publisher's web page to pre-order the book or to obtain further details on its publication date.

A draft, pre-publication copy of the book can be found below. This draft copy is made available for personal use only and must not be sold or redistributed.

This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.

This paper answers Bell’s question: What does quantum information refer to? It is about quantum properties represented by subspaces of the quantum Hilbert space, or their projectors, to which standard (Kolmogorov) probabilities can be assigned by using a projective decomposition of the identity (PDI or framework) as a quantum sample space. The single framework rule of consistent histories prevents paradoxes or contradictions. When only one framework is employed, classical (Shannon) information theory can be imported unchanged into the quantum domain. A particular case is the macroscopic world of classical physics whose quantum description needs only a single quasiclassical framework. Nontrivial issues unique to quantum information, those with no classical analog, arise when aspects of two or more incompatible frameworks are compared.

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. [1]

Footnotes

[1]

G. B. Lesovik, A. V. Lebedev, I. A. Sadovskyy, M. V. Suslov, and V. M. Vinokur, “H-theorem in quantum physics,” Scientific Reports, vol. 6. Springer Nature, p. 32815, 12-Sep-2016 [Online]. Available: http://dx.doi.org/10.1038/srep32815

Learn about quantum computation and quantum information in this advanced graduate level course from MIT.

About this course

Already know something about quantum mechanics, quantum bits and quantum logic gates, but want to design new quantum algorithms, and explore multi-party quantum protocols? This is the course for you!

In this advanced graduate physics course on quantum computation and quantum information, we will cover:

The formalism of quantum errors (density matrices, operator sum representations)

This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

Springer recently announced the publication of the book Quantum Biological Information Theory by Ivan B. Djordjevic, in which I’m sure many readers here will have interest. I hope to have a review of it shortly after I’ve gotten a copy. Until then…

From the publisher’s website:

This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects.

Integrates quantum information and quantum biology concepts;

Assumes only knowledge of basic concepts of vector algebra at undergraduate level;

Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology;

Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models on tumor and cancer development, quantum modeling of bird navigation compass, quantum aspects of photosynthesis, quantum biological error correction.

In a lecture at Caltech, Brian Swingle reviews the idea that entanglement is the glue which holds spacetime together and shows how Einstein's equations plausibly emerge from this perspective. One ubiquitous feature of these dynamical equations is the formation of black holes, so he concludes by discussing some new ideas about the nature of spacetime inside a black hole.

Brian Swingle Colloquium at Caltech

From the Physics Research Conference 2015-2016
on Thursday, November 19, 2015 at 4:00 pm
at the California Institute of Technology, East Bridge 201 – Norman Bridge Laboratory of Physics, East