Mini course SS2019: Quantum Entropy and its Applications

Lectures and Exercises: H. Chau Nguyen (email)

Time and place: 14:00-16:00 Wednesday, Room D115-ENC.


  • Basic intuitive knowledge of quantum mechanics
  • Basic concepts of general algebra and linear algebra


  • Classical and quantum systems: observables and states
  • Definition of entropy
  • The statistical interpretation of entropy
  • Quantum processes
  • Monotonicity of the relative entropy: the statement and the consequences
  • Monotonicity of the relative entropy: lessons from the proof
  • Bipartite system: subadditivity, mutual information, conditional entropy
  • Application: the classical capacity of communication channels
  • Application: thermodynamics entropy and the Landauer’s principle
  • Multipartite system: strong subadditivity

Scripts (password required):

Exercises: integrated in the classes


  • Petz, D., “Quantum information theory and quantum statistics”, Springer 2008.
    The content is generally good, but one has to be careful with some technical definitions and typos.
  • Ohya, M. and Petz, D., “Quantum entropy and its use”, Springer 1993.
    This is a somewhat advanced version of the above one. The contents are much richer, but also a lot denser.
  • Nilsen, M. A. and Chuang, I. L. “Quantum computation and quantum information”. Cambridge 2010.
    This book is kind of classic. The contents are rich, but the structure is perhaps not optimal.
  • Cover, T. and Thomas, J. A., “Elements of information theory”, John Wiley & Son 2006.
    Classics for information theory: rich, clean, clear.