VU: Resource theories and thermodynamics (March 11 - June 24, 2020)

Due to the Corona crisis, there are currently no actual lectures. However, you can participate remotely -- see below for the rules.
In particular, every Wednesday from 15:00 - 16:00, there will be a video chat where you can talk to us in person.
Here is the link:
All you need is a computer with a camera and a microphone; no login required. This is your opportunity to talk to us in person, to ask us questions about the lecture and exercise material, and to give us feedback (please do!).

Lecturers: Dr. Markus P. Müller, Dr. Andrew J. P. Garner, Dr. Felix Binder.

(drawing and copyright by Lidia del Rio)

Updated organization due to the Corona virus crisis:
Since we cannot give lectures or tutorials in person, we decided to do the following.

- Every week, there will be lecture notes that you can (and should) read and study, see below for download. These contain the material that we would have told you in the lecture and the tutorial.
- Furthermore, there will be one exercise sheet per week that you can solve. Over the course of the semester, please hand in the solutions to at least 4 of the exercise sheets. Please scan your solutions, or take mobile phone pictures, and send them to us by email. You may, and are actually encouraged, to work in groups of up to 3 people (as long as you follow the Corona guidelines and don't meet in person, but, say, via Skype). Please hand in only one set of solutions per group.
We will grade these sheets, and give you a certain number of points, depending on your answers. In order to determine your final grade, we will take into account the 4 best solutions to exercise sheets that you have sent us over the semester. You need 60% of the points on those sheets to pass, and more points means better grades.
- For the final grade, we will determine the average percentage of points that you have obtained on your four best exercise sheets. This leads to the following marks:
   90% or more: 1 (very good)
   80% or more, but less than 90%: 2 (good)
   70% or more, but less than 80%: 3 (satisfactory)
   60% or more, but less than 70%: 4 (sufficient)
   less than 60%: 5 (insufficient).
- In addition to the video chat (see above), you can always email us for questions.

Our email addresses are: (Markus Müller), (Andy Garner), (Felix Binder).

A final request: Please let us know how easy or difficult the lectures and the exercises are for you, so that we can get an idea of your background and adjust the level accordingly.

Lecture notes (handwritten and scanned):

  • Lecture 1 (March 11): Overview on the lecture series; folklore derivation of Landauer's principle; basics of mixed quantum states and  entropies; some exercises.

  • Lecture 2 (March 18): A rigorous version of Landauer's Principle; end of part 1 of the course (see overview below). Motivation for and definition of the resource theory of nonuniformity.
    See also this excellent essay on the Szilard engine by Andy Garner.

  • Lecture 3 (March 25): Majorization and Lorenz curves, nonuniformity (N.U.) monotones, distillable N.U. and N.U. of formation, the trace distance, smooth entropies.

  • Lecture 4 (April 1): Approximate formation/distillation of pure bits, state conversion in the thermodynamic limit, typical subsets, asymptotic equipartition property, Shannon's noiseless coding theorem. End of part 2 of the course.
    Note: Section 2.12 (Typical subsets, AEP, data compression) is optional! You don't need to understand this for the rest of the lecture or the exercises. I'm giving you an overview on these topics because they are the reason why the smoothed Rényi-0 and Rényi-infinity entropies converge to the "standard" Shannon entropy in the limit. In other words: information theory and data compression are the reason why we will recover the standard thermodynamic laws in the thermodynamic limit.
    For those of you who want to know more, here are some possible references:
    -- Cover, Thomas, Elements of Information Theory, John Wiley & Sons, 2006. (Well-known and well-written book on the basics of information theory)
    -- The Wikipedia entry (oh well, yes, indeed).
    -- Shannon's original 1948 paper.
    Note that "AEP" is for "asymptotic equipartition property": the property that typical outcome sequences, in the limit of large n, will all have approximately the "same" probability (close to 2^(-nH)). It is also the name of our lemma in Section 2.10, because it's mathematically closely related.

  • Lecture 5 (April 22): Quantum teleportation, superdense coding. General structure of quantum resource theories: free states and operations, convexity, tensor product structure.

  • Lecture 6 (April 29): The Resource Theory of Entanglement. [Some small corrections added on April 30.]

  • Lecture 7 (May 6): Asymptotic entanglement conversion, Resource monotones & measures, entanglement monotones, entropy of entanglement. [Some small corrections added on May 8.]

  • Lecture 8 (May 13):  Passivity, thermality, and the Gibbs state. End of part 3 of the course.

  • Lecture 9 (May 20): Recap of passivity, definition of the resource theory of athermality; zeroth law; heat baths unlock state transitions; transition rates in the thermodynamic limit: recovering the free energy. [Some small corrections added on May 25.]

  • Lecture 10 (May 27): Recap of previous lecture; reducing thermal operations to the classical case (for blockdiagonal states only), d-majorization, d-Lorenz curves. [Some small corrections added on May 26.]

  • Lecture 11 (June 3): The Rényi divergences, work cost: the max-free energy, extractable work: the min-free energy, approximate transitions: smoothing.

  • Lecture 12 (June 10): Comparison of two resource theories; catalysis in the RT of nonuniformity and in the RT of athermality; the "second laws" of (quantum) thermodynamics.

  • Lecture 13 (June 17): Coherence in the resource theory of athermality. Time-translation symmetry and thermodynamics; thermal operations versus Gibbs-preserving maps; free energy and asymmetry monotones.

  • Lecture 14 (June 24): If you have followed the course, then you will now see that you are able to read and understand actual research papers in the field. Start by reading part of the following (famous) paper: J. Åberg, Catalytic coherence, Phys. Rev. Lett. 113, 150402 (2014), download here.
    It is enough if you read the main text (4 pages), and you can also skip the part on the half-infinite ladder. You should be able to understand most of what's written.
    After this, please watch the talk that I've given in this year's "Thermodynamics for Young Scientists" workshop in Bad Honnef: slides for download.
    On the one hand, this gives you a (hopefully) nice recapitulation of parts of the course with some pictures. On the other hand, it explains some of my own research (on catalysts, correlations and the free energy), and relates this as well to Åberg's paper.

Exercise sheets

There are 10 sheets in total. If you hand in an exercise after the due date, then we will mark it for your information, but the points will not be counted.
Some problem sets include optional parts. Points on these questions count as bonus points. When determining the percentage of points on a given problem set, these bonus points count in the enumerator, but not in the denominator. In this way, you can achieve more than 100% on some of the problems sets.

Overview on the course

The course will consist of the following four parts:

1. Introduction: Landauer's Principle and basics of quantum information theory
2. The resource theory of nonuniformity: Motivation, definition; majorization, Lorenz curves, single shot and asymptotic state conversion
3. The resource theory of entanglement: LOCC operations, Nielsen's theorem, catalysis; general definition of resource theories
4. Thermodynamics as a resource theory: Extractable work and work cost; d-majorization; the "many second laws"; the role of quantum coherence

Last edit: June 20, 2020