Quantum Information Theory
Summer 2018.
Lecture & Exercise: Mondays 10.0011.30
(New Theory Building 0.03),
Wednesdays 12.0013.30
(New Theory Building 0.03).
Excercises every second week, for an average of three contact hours of lecturing and one contact hour per week of exercises.
Lecturer: David Gross; Exercises: Mateus Araújo .
Announcements
 The project descriptions are now available. They should be done in groups of three, and at the end of the semester the group must give a 30 minutes presentation about it. Please send an email to Mateus Araújo and David Gross saying which project you want to do. If demand exceed the three projects described, we can come up with more.

Video link to Bonn: Dial into our conferencing machine using the IP address 134.95.67.246.

Link to Illias message board. The future has arrived!
Course description
The fundamental differences between quantum mechanics and the classical description of the world has lead early researchers to describe the theory in almost mythical terms.
In the past 20 years, quantum information theory succeeded in demystifying many counterintuitive phenomena, by turning them into quantitative questions about precisely defined tasks for information theory and theoretical computer science.
For example, instead of musing about how to interpret the "spooky action at a distance" that quantum mechanics seems to imply, we can now calculate at which bit rate one can extract secret keys for cryptographic purposes from entangled states shared between two parties.
We will start by reintroducing quantum mechanics from a more abstract pont of view than usually done in Bachelor QM courses.
(Thus, strictly speaking, no prior knowledge of QM is necessary  though it would be helpful).
Based on this, we will treat the fundamental protocols of quantum communication and quantum computation.
Covered Topics
 The structure of quantum mechanics
 A first example: Quantum Teleportation
 Finitedimensional quantum systems, tensor products, density matrices, partial trace, unitary gates, quantum circuits
 Entanglement, Bell Inequalities and the two levels of the NoCloning Theorem
 Quantum Information
 Intro to information theory: Entropies, channel capacities, random coding
 Quantum communication theory: Quantum channels, stabilizer codes
 Quantum key distribution
 Quantum Computation
 Grover's algorithm
 Classical Public Key cryptography (about that green padlock in your browser)
 Shor's algorithm
 Brief intro to (quantum) complexity classes
Prerequisites
Linear algebra.
Basic knowledge of quantum mechanics won't hurt. Beyond that, the course will be selfcontained.
Material
Occassionally, when my notes feel clean enough, I will post them here.
However, these will usually be late, unreadable, and incomplete and therefore not a substitute for full lecture notes.
Literature
 Nielsen & Chuang, Quantum Information and Quantum Computation

Lecture notes by John Preskill.
Exercises