Teaching plan for the course unit



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General information


Course unit name: Quantum Information Theory

Course unit code: 574636

Academic year: 2021-2022

Coordinator: Bruno Julia Diaz

Department: Department of Quantum Physics and Astrophysics

Credits: 6

Single program: S



Estimated learning time

Total number of hours 150


Face-to-face and/or online activities



-  Lecture

Face-to-face and online




-  Lecture with practical component

Face-to-face and online



Independent learning






  1. Solid knowledge of probability, random variables and linear algebra. 



Learning objectives


Referring to knowledge

  1. To acquire a solid background in the theory of quantum information regarding mathematical tools and  basic concepts.

  2. To be able to solve problems  concerning preparation, manipulation and measurement of isolated and composite quantum systems. 

  3. To become familiar with the basic information measures and typicality both in the classical and in the quantum context. 

  4. To understand the fundamental limitations of the communication of classical information over classical and quantum channels.

  5.  To become familiar with the basic quantum error correction codes.

  6. To understand the quantum cryptography principles and become familiar with the basic quantum key distribution protocols.



Teaching blocks


1. Principles of quantum information


  1. Quantum formalism revisited: Hilbert spaces and linear algebra. Dirac notation.

  2. Description of quantum states. The qubit. 

  3. Quantum theory of measurement. 

  4. Ensemble of quantum states and density matrix formalism. Purification

2. Quantum protocols, algorithms and channels


  1. Quantum maps, quantum channels and quantum instruments. 

  2. Quantum channels: examples and applications.

  3. Quantum protocols/algorithms: Deutch-Jozsa, Grover, Fourier.

3. Entanglement theory


  1. Composite quantum systems. Basics concepts on entanglement.

  2. Using entanglement: dense coding and quantum teleportation.

  3. Entanglement in mixed states: measures and uses.

  4. Non-locality and Bell inequalities.

4. Classical entropy and information


  1. Entropy, conditional entropy and joint entropy.

  2. Fano’s inequality

  3. Mutual information, conditional mutual information and relative entropy.

  4. Markov chains and data processing inequality.

  5. Shannon Channel coding theorem.

5. Quantum entropy and information


  1. Quantum entropy and joint entropy.

  2. Conditional quantum entropy and coherent information.

  3. Quantum mutual information and conditional quantum mutual information.

  4. Quantum data processing inequality.

  5. Trace norm, trace distance and fidelity. The AFW inequality.

6. Classical communication over quantum channels


  1. Accessible information.

  2. The information of quantum channels.

  3. The Holevo-Schumacher-Westmoreland theorem.

  4. Quantum Capacity examples



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



Examination-based assessment

Final exam covering all the contents of the course



Reading and study resources

Consulteu la disponibilitat a CERCABIB


Michael Nielsen and Isaac Chuang. Quantum Computation and Quantum Information. Tenth Anniversary Edition. Cambridge University Press 2010.  EnllaƧ

Mark M. Wilde. Quantum Information Theory, Second Edition. Cambridge University Press 2017.   EnllaƧ

Preprint version available  EnllaƧ

Thomas Cover and Joy A. Thomas, Elements of Information Theory, Second Edition. Willey 2006.  EnllaƧ

Abbas El Gamal and Young-Han Kim. Network Information Theory. Cambridge University Press 2011.

Matthieu Bloch and Joao Barros. Physical-Layer Security. Cambridge University Press 2011.


Peter W. Shor and John Preskill. Simple Proof of Security of the BB84 Quantum Key Distribution Protocol. Phys. Rev. Lett 85, 441.

Web page

Preskill lectures on Quantum Information (on the web)

John Watrous notes on Quantum Information   EnllaƧ