Resources

Lecture Notes

Lecture notes will be provided during the lecture.

An updated version is available here  (25/01/2012: complete script, including chapter 8 on Bell inequalities and non-locality).

Mistakes and typos should be reported to Lídia.

Later in the semester:

Slides on resource inequalities here (see also chaper 5 of the lecture notes).

All about Bell inequalities in Roger Colbeck's lecture notes, here.

Talk of the week, in the loose sense of "week"

Video recordings of interesting and accessible talks on quantum information, quantum computation and quantum cryptography.

Week 1: Spin Glasses and Computational Complexity, by Daniel Gottesman.

A neat introduction to complexity theory and quantum computation. You don't need any background in quantum information to follow it.

Week 2: Lectures on Foundations of Quantum Mechanics, by Rob Spekkens.

Never really happy about the postulates of quantum mechanics? Well, neither are researchers. This is a comprehensive and well-motivated account of current research on foundations.

Week 3: Position-based quantum cryptography: impossibility and constructions, by Serge Fehr.

A very nice idea and all the reasons it could never work.

Week 4: Verschlüsseln mit Verschränkung, by Matthias Christandl.

In German; no idea what he's saying.

Weeks 5 to 10: Foundations, foundations, foundations!

Perimeter Institute (Waterloo, Canada) held a workshop on Foundations of Quantum Mechanics last year. The videos of all the talks are available here. Here's a quick, biased selection:

Opening welcome, by Giulio Chiribella.

Is information the key?, by Gilles Brassard.

A light-hearted introduction to the topic. Very light-hearted.

How Fundamental is the Uncertainty Principle?, by Renato Renner.

A little introduction to a recent result on the uncertainty principle in the presence of a quantum memory. He also talks about applications of quantum information to thermodynamics. If you're interested in these topics, we actually know something about them.

Is the universe exponentially complicated? A no-go theorem for hidden variable interpretations of quantum theory., by Jonathan Barrett.

Does there exist an interpretation of quantum theory such that (i) the state vector merely represents information and (ii) the underlying reality is simple to describe (i.e., not exponential)? In this beautiful talk, Jonathan shows that the answer is no.

Does ignorance of the whole imply ignorance of the parts?, by Stephanie Wehner.

In other words, does high entropy about a bipartite system imply high entropy about the individual subsystems? It sounds intituitive it should be so, and for classical systems that is indeed the case. There are, however, quantum states that violate this intuition arbitrarly.

Randomness amplification, by Roger Colbeck.
A nice follow-up to the lecture on 'quantum theory cannot be extended' we had a few weeks ago. The goal is to create 'free' randomness, ie. a random bit string that is not correlated with anything else in the universe (and cannot be predicted by any adversary). Can we do this starting from a system that is somewhat correlated with the adversary?

You can also check several different axiomatic approaches to quantum mechanics, for instance by Lucien Hardy, Paolo Perinotti and Markus Müller.

Literature

Classical Information Theory

• Thomas M. Cover and Joy A. Thomas, "Elements of Information Theory", Wiley Series in Telecommunications.
  Available electronically: http://www3.interscience.wiley.com/cgi-bin/bookhome/110438582
  (accessible from within the ETH domain only)

Quantum Information Theory

• Michael A. Nielsen and Isaac L. Chuang, "Quantum Computation and Quantum Information", Cambridge University Press.  (available in the physics library)
• John Preskill's lecture notes on "Information for Physics".
  Available electronically: http://www.theory.caltech.edu/~preskill/ph229/#lecture

FAQ

Feel free to send us your questions about the script, exercises or contents of the course in general.

We will publish here some of the questions and answers.

Measurements 

I'm confused with the notion of measurement. Sometimes, we speak about doing a measurement "represented by the observable O=sum...", sometimes we say "do a measurement with respect to the basis {...}" and finally there is also the version "do a measurement with respect to the POVM {...}". I don't see the link between these three methods of measuring a state.
Moreover, I have a problem for each of these variants...

Full question and response in this file.

Locality and nonclassicality of quantum theory

I have two questions about the topic "quantum nonclassicality" as discussed in the script.
On p. 51, the proof that QM is in general not classically local is mentioned (i.e. proof of Lemma 5.3.1). However, I don´t get a few things...

Full question and response in this file.