Notes

See here for a preliminary version of the textbook “Principles of Quantum Communication Theory: A Modern Approach”, coauthored with Mark Wilde.

Below, you’ll find links to the notes I’ve written on various aspects of mathematics, quantum theory and quantum information theory.

1. Quantum States and Channels
2. Quantifying quantum causal networks (PDF; contains a review of quantum causal networks/quantum combs/quantum strategies, as well as definitions of information quantities and resource measures for them.)
3. Pauli channels (PDF; definition and basic properties of n-qubit Pauli channels.)
4. Symmetric Extendability of Quantum States
5. Quantum states from graphs (See here for more details on graph states.)
6. Random quantum states (PDF; contains a development of the theory of random pure states, starting with a calculation of the volume of the space of all pure states. We also determine the probability density of the probability distribution obtained by measuring a random pure state.)
7. Analysis of the BB84 and six-state QKD protocols (PDF; provides details on some of the simplifying steps of the two QKD protocols. In particular, it shows how the parameter estimation portion of the protocols can be reduced to the estimation of just one parameter, often called the Quantum Bit Error Rate (QBER).)
8. A Compact Fermion-to-Qubit Mapping (PDF; slides for a presentation at LSU’s QST group meeting in April 2021, based on the papers arXiv:2003.06939 and arXiv:2101.10735.)
9. Group Theory (PDF; lecture notes based on the course PMATH 336 at the University of Waterloo in Summer 2012.)
10. Functional Analysis (PDF; lecture notes based on the course AMATH 731 at the University of Waterloo in Fall 2014.)

If you suspect there are errors, please don’t hesitate to contact me. Please note that the two lecture notes posted above are incomplete to an extent and follow very closely some of the standard textbooks on the subjects. The purpose of typing the notes was to combine content from several different textbooks, add clarifying points often missing in these books, and to format the content in a manner that is (hopefully) more easy to follow.

Lectures on Quantum Communication Theory

In November 2019, I delivered a series of five lectures on quantum communication theory at the International Institute of Physics in Natal, Brazil. Here is a summary of the course topics. Video recordings of the lectures can be found here. Below are my handwritten lecture notes in PDF format.

• Lecture 1: Introduction, quantum states, quantum channels, measurements.
• Lecture 2: Quantum teleportation and superdense coding
• Lecture 3: Entanglement-assisted classical communication
• Lecture 4: Quantum communication
• Lecture 5: Private classical communication and quantum key distribution. More details on reducing the parameter estimation portion of the BB84 and six-state protocols to the estimation of just one parameter can be found in this document, which is part of a more detailed development that can be found in this paper.