Teaching plan for the course unit

 

 

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General information

 

Course unit name: Advanced Quantum Information Theory

Course unit code: 574640

Academic year: 2021-2022

Coordinator: Bruno Julia Diaz

Department: Department of Quantum Physics and Astrophysics

Credits: 3

Single program: S

 

 

Estimated learning time

Total number of hours 75

 

Face-to-face and/or online activities

26

 

-  Lecture

Face-to-face and online

 

20

 

-  Lecture with practical component

Face-to-face and online

 

6

Independent learning

49

 

 

Recommendations

 


  1. Students should know the basic quantum mechanics and quantum information theory as provided in the MSc. 

  2. Further recommended knowledge: probability theory. 

 

 

Competences to be gained during study

 


  1. Understanding one-shot information processing tasks

  2. Understanding the mathematical tools to analyse one-shot protocols

 

 

 

 

Learning objectives

 

Referring to knowledge


  1. Broad perspective of quantum information theory, especially one-shot information theory. 

  2. Become familiar with the basic tools of formalism: min- and max-entropies, Rényi entropies and relative entropies

  3. Understand the basic tasks and protocols; decoupling, hypothesis testing, convex-split lemma, position-based coding. 

 

 

Teaching blocks

 

1. Classical communication

*  


  1. Quantum channels

  2. One-shot communication, plain and entanglement-assisted

  3. Coding theorems via hypothesis testing

  4. Converse bounds from generalised divergences

  5. Application to memoryless channels: Holevo capacity & strong converse

2. Zoo of one-shot entropic quantities

*  


  1. Relative entropies

  2. …and their derived entropies and conditional entropies

  3. Interlude on semidefinite programming (SDP)

  4. Asymptotic equipartition theorems (AEP)

3. Quantum data compression

*  


  1. One source: max-entropy

  2. Correlated source: conditional max-entropy

  3. Decoupling principle

  4. Decoupling via convex-split lemma

4. Quantum communication

*  


  1. Turning static (data compression) protocols into dynamic ones for channels

  2. Strong converses and pretty strong converses

5. Private communication

*  


  1. Quantum wiretap channel

  2. Coding theorem via hypothesis testing and decoupling

 

 

Teaching methods and general organization

 


  1. Lectures where theoretical contents of the subject are presented. 

  2. Practical exercise classes in which students may participate. 

  3. Activities related to the subject suggested by the teaching staff. 

 

 

Official assessment of learning outcomes

 


  1. Evaluation of written exercises.  

  2. Written or oral examination. 

  3. Individual projects, e.g. report on a specific quantum sensing technology.

  4. Participation.   

 

 

Reading and study resources

Consulteu la disponibilitat a CERCABIB

Book

  1. Michael A. Nielsen and Isaac L. Chuang. "Quantum Computation and Quantum Information"

Thomas M. Cover and Joy A. Thomas Elements of Information Theory

  1. John Preskill, Lecture notes

A Quantum Leap in Information Theory ,  Stefano Mancini and Andreas Winter

Quantum Information Processing with Finite Resources, Tomamichel, Marco

Sumit Kathri and Mark M. Wilde, Principles of Quantum Communication Theory: A Modern Approach, 
arXiv:2011.04672