Quantum Information Theory

Summer 2018. Lecture & Exercise: Mondays 10.00-11.30 (New Theory Building 0.03), Wednesdays 12.00-13.30 (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 counter-intuitive 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 re-introducing 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
    • Finite-dimensional quantum systems, tensor products, density matrices, partial trace, unitary gates, quantum circuits
    • Entanglement, Bell Inequalities and the two levels of the No-Cloning 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 self-contained.

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