COMP-761: Quantum Information Theory

 

Time: Tuesday and Thursday from 8:300 to 10:00 (Winter 2006)

Room: McConnell 320

 

Instructor:      Patrick Hayden

                        Office: ENGMC 108N

                        Phone: 398-5491

                        Email: patrick@cs.mcgill.ca

                        Office hours: By appointment

 

Course description:

 

This course will present the quantum analog of Shannon’s information theory. This area has seen an explosion of interest and a correspondingly rapid technical advance over the past ten years, largely in response to the development of quantum-mechanically based cryptographic protocols and Shor’s famous algorithm for factoring integers. The unavoidable presence of noise in any quantum-mechanical information processing device means that error-correction techniques will play a crucial role in any practical application of quantum cryptography or computing. This course will focus on asymptotic protocols for compression, communication, error correction and state distillation, identifying the absolute limits placed on those tasks by quantum mechanics.

 

Familiarity with quantum mechanics is recommended. The course content is very mathematical, but elementary. Students should be comfortable with basic probability theory, linear algebra and real analysis. The material will be covered through a combination of lectures and student presentations.

 

Course outline:

  • Classical information theory:
    • Compression: Shannon’s noiseless coding theorem
    • Error correction: Shannon’s noisy coding theorem
  • The birth of the qubit: Schumacher compression
  • Tools for quantum information:
    • Review of quantum-mechanical formalism (including Bell’s theorem)
    • Inequalities for von Neumann entropy
    • Strong subadditivity
  • Three brilliant trivialities:
    • Superdense coding
    • Teleportation
    • Coherent classical communication
  • The HSW theorem: classical data through a noisy quantum channel
  • A noiseless interlude:
    • Superdense coding of quantum states and its consequences
    • Majorization and entanglement manipulation
  • The family of quantum protocols
    • The mother, father and fully quantum Slepian-Wolf protocols
    • Everyone else
      • Entanglement distillation
      • State merging
      • Entanglement-assisted and quantum capacities
      • Quantum reverse Shannon theorem

 

Grading: 65% assignments and 35% presentations.

 

Text: There is no text for the course. However, roughly the first month’s worth of material can be found in Quantum Computation and Quantum Information by Nielsen and Chuang, which is an excellent introduction to the field as a whole. Several copies should be available in the university bookstore.

 

Presentations: More information can be found here.

 

Assignments:

Assignment 1: Due Friday, February 3

Assignment 2: Due Tuesday, February 28

Assignment 3: Due Thursday, March 16
Assignment 4: Due Thursday, March 30

Assignment 5: Due Monday, April 10

 

Embarrassing obligatory inclusion:   

By the direction of Senate (January 29, 2003), all course outlines have to include the following statement:

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).