Feel free to reach me by e-mail if you have any doubts or questions .

Quantum Information, 2022-23 (Tutorials, FU Berlin)

Students can send me the week’s exercises (photos of the sheets or notes written on tablet) via e-mail . For my tutorial, the usual deadline for submitting the exercises is Sunday at 11:59 pm.

Email me if you would like to be added to the mailing list that I will use for quick communications related to my tutorials. This webpage can be useful for the students especially to have the tablet notes that I write and use for my tutorials.


  • Problem Sheet 0: “Warm-up”. (PDF, Solutions)

  • Problem Sheet 1: “Density matrices and Bell experiments”. (PDF, Solutions)

  • Problem Sheet 2: “POVMs and encoding classical information”. (PDF, Solutions)

  • Problem Sheet 3: “Quantum Teleportation and p-norms”. (PDF, Solutions)

  • Problem Sheet 4: “Graphical calculus and Quantum Channels”. (PDF, Solutions)

  • Problem Sheet 5: “More Quantum Channels and Entropy”. (PDF, Solutions)

  • Problem Sheet 6: “Operator Properties and LOCC”. (PDF, Solutions)

  • Problem Sheet 7: “Capacities and Majorization”. (PDF, Solutions)

  • Problem Sheet 8: “Entanglement Witnesses and Cryptography”. (PDF, Solutions)

  • Problem Sheet 9: “Quantum Fourier Transform and Stabilizers”. (PDF, Solutions)

  • Problem Sheet 10: “More stabilizers and quantum gates”. (PDF, Solutions)

Here are some additional notes used in my tutorial:

  • “PVM, POVM and Naimark dilatation theorem”. (PDF)
  • “Quantum Channels Theorems”. (PDF)
  • “Classical Entropies”. (PDF)
  • “Quantum Entropies”. (PDF)
  • “Basics of quantum computing”. (PDF)
  • “Stabilizer formalism”. (PDF)


The main page of the course is here, where you can find the Lecture notes of the course written by Jens Eisert.

Other good Quantum Information notes are for example those written by Michael M. Wolf PDF, those written by John Preskill PDF and those written by Joseph M. Renes PDF.

The book written by Nielsen & Chuang can be found here.

A good reference for Information Theory is the book of Cover & Thomas PDF, while a good reference for Quantum Shannon Theory is Mark Wilde’s book PDF.