Lecture: Quantum information theory (20110401)

• Lecturer: Jens Eisert
  
  
• On-site format: The lecture will be held on-site.
  
  
• Place, date and time:
  Monday 14:15-16:00  (0.1.01 Hörsaal B).
  Thursday 14:15-16:00 (1.3.14 Hörsaal A).
  
  
• Exam date and time:
  To be announced.
  
  
• Second exam date and time:
  To be announced.
  
  
• Tutorials: We offer three tutorials:
  - Monday 12:15-13:45 (1.4.03 Seminarraum T2)
  - Monday 16:15-17:45 (1.4.31 Seminarraum E3)
  - Tuesday 16:15-17:45 (1.1.16 FB-Raum)
  
  
• Tutors:
  - Elies Gil-Fuster: e.gilfuster@fu-berlin.de
  - Roberto Losada: roberto.losada@fu-berlin.de
  - Moritz Scheer: moritz.scheer@fu-berlin.de
  - Gregory White: gregory.white@fu-berlin.de
  
  
• Problem sheets:
  - The exercise sheets will be uploaded weekly to this website, on Thursday afternoon.
  - The solved exercise sheets must be submitted before the next Thursday lecture, via email to all four tutors.
  
  • Exercise sheet 0 (solutions)
  • Exercise sheet 1 (solutions)
  • Exercise sheet 2
  • Exercise sheet 3
• Topic of the lecture: 

  This course provides an overview of an exciting and emerging field of research: quantum information theory and quantum technologies. The field is driven by the observation that single quantum systems, when used as elementary carriers of information, enable entirely new modes of information processing and communication—modes that differ fundamentally from their classical counterparts. Quantum key distribution, for example, allows communication in a manner that is secure against eavesdropping by unauthorized parties. Quantum simulators have the potential to outperform classical supercomputers in certain simulation tasks. Meanwhile, quantum computers—once only anticipated but now rapidly developing—can solve not all, but specific computational problems that remain intractable for classical machines. This course offers a comprehensive overview of these developments. At its core is a focus on methodological foundations, building on the principles of quantum theory. At the same time, we emphasize that quantum information is not merely about information processing, but also represents a powerful conceptual framework—a mindset that can be applied to problems in other fields, most notably in condensed matter physics, with which it is deeply intertwined. Finally, we will explore modern and recent advances in this rapidly evolving area.

• Content:
  
  1. Introduction
  1.1 Some introductory words
  1.2 Quantum information: A new kind of information?
  
  2. Elements of quantum (information) theory
  2.1 Quantum states and observables
  2.2 Unitary time evolution
  2.3 Composite quantum systems
  
  3. Two possible machines
  3.1 Quantum teleportation
  3.2 Dense coding
  
  4. Quantum channels and operations
  4.1 Complete positivity
  4.2 Kraus theorem
  4.3 Local operations and classical communication
  
  5. Entanglement theory
  5.1 Pure state entanglement
  5.2 Mixed state entanglement
  
  6. Quantum Shannon theory
  6.1 Capacities as optimal rates
  6.2 A glimpse at quantum Shannon theory
  
  7. Quantum key distribution
  7.1 BB84 scheme
  7.2 Entanglement-based schemes
  7.3 Words on quantum technologies
  
  8. Elements of quantum computing
  8.1 Why quantum computing?
  8.2 From classical to quantum computing
  8.3 Gottesman-Knill and Solovay-Kitaev theorems
  
  9. Quantum algorithms
  9.1 Deutsch and Deutsch-Jozsa algorithm
  9.2 Grover’s database search algorithm
  9.3 Exponential speed-up in Shor’s factoring algorithm
  9.4 Quantum algorithmic primitives and modern developments
  
  10. Quantum computational models
  10.1 Adiabatic quantum computing
  10.2 Measurement-based quantum computing
  10.3 Further models of quantum computing
  
  11. Quantum error correction
  11.1 Peres Code
  11.2 Shor code
  11.3 Elements of a theory of quantum error correction
  11.4 Stabilizer codes and the toric code
  
  
• Literature: See the script.

• Lecturer: Jens Eisert
• Date and time: Contact the lecturer.