ITP Lecture Archive

Quantum Information Theory – FS 2011

Lecture: Prof. Renato Renner

Thursday 12:45-14:30, HIT F11.1

Exercise Session : Lídia del Rio (HIT F11.1) and Normand Beaudry (HIT H51)

Thursday 14:45-15:30

Download all documents (zip, 6.8 MB).

Study materials

Lecture Notes

Lecture notes will be provided during the lecture.

An updated version is available here (download, 16/08/2011).

Mistakes and typos should be reported to Lídia.

Slides of the lecture on resource inequalities (download, needs another update (soon)).

Talk of the week

Here we will post links to 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 week. 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.

If you're missing Renato already. :) 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, and can discuss them in the lecture or exercise class.

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.


Classical Information Theory
Quantum Information Theory





Note: The solutions for series 8 may be coming a little too late.


Basis of the exam is the lecture, the script (Chapter 1-6), and the exercises. For the chapter about "Resource Inequalities", the exam will solely be based on the material covered in course (i.e., the slides). The corresponding chapter in the lecture notes can be considered as a supplement (see remark at the beginning of Chapter 7).

Non-local correlations (and Bell inequalities) will not be covered in the exam.


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.


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.

Course certificate (Testat)

There will be 11 exercise series, each with 3 exercises. In order to get a course certificate you need to hand in 26 exercises.

Exercises extremely well solved count double (if not obviously copied from previous years).

When exercises have several parts (a, b, c, etc.), solving one of the parts is enough to count as one exercise.

You have to solve the exercises individually (no groups, except for series 10).

Exercises are published every Thursday and should be handed in one week later.

You should have your Testat by now. Contact us if there is any problem.