Teaching

I am currently lecturing the first section of the Mathematics for Quantum Information masters course given in the mathematics faculty of the Universidad Complutense de Madrid

My hand-written lecture notes are now available on this page. Note that, though I have checked the notes for typos and mistakes, that by no means guarantees there are none! If you think you've spotted one, let me know.

(If you're looking for the lecture notes for the quantum mechanics course I lectured in Bristol in 2009 and 2010, they're still available here. If you're looking for the material I prepared for classical mechanics and electrodynamics courses taught by Prof. Weise at the TUM quite a few years ago now, it's still available here.)

Lecture Notes

	Lecture 1 Section 0: Dirac notation; Section 1: The postulates of quantum mechanics
	Lecture 2 Section 2: Combining quantum systems: tensor products
	Lecture 3 Section 3: Non-locality and Bell inequalities
	Lecture 4 Section 4: Ensembles and density operators; Section 5: Taking quantum systems apart: reduced states and the partial trace; Section 6: A brief introduction to entropy

Recommended books

I have closely followed Chapter 2 of Nielsen and Chuang (which is by now the standard textbook on quantum information theory), with some additional mathematical content, and a more careful proof of the CHSH inequality.

The other books listed below may also be of interest.

"Quantum Computation and Quantum Information", Nielsen & Chuang: Chapter 2 gives a concise but excellent introduction to quantum mechanics, more suitable for quantum information theory than most quantum mechanics textbooks. I have closely followed this chapter, but I have given additional mathematical results and proofs when desirable. Bell inequalities are also covered in this chapter, but this is not the focus of the book and the proof they give obscures some of the subtleties.
"An Introduction to Quantum Theory", Hannabuss: A nice and more mathematically oriented quantum mechanics textbook, but still contains a lot more physics than covered in this course.
"Quantum Theory: Concepts and Methods", Asher Peres: A delightful text book that contains a good treatement of the Bell experiment and much more.
"Bell Inequalities and Entanglement", Werner and Wolf, arXiv:quant-ph/0107093: This review article gives a careful and rigorous discussion of Bell inequalities.
"Speakable and Unspeakable in Quantum Mechanics", John Bell: A collection of insightful essays and papers by John Bell (of Bell inequality fame).
"Feynman Lectures vol. 3", Feynman, Leighton, Sands: Not so useful for covering the course material, but as an accompaniement to the lecture notes or other textbooks, volume 3 of Feynman's famous lecture series contains a presentation of quantum mechanics with a very different and less mathematical flavour, which some may find interesting.