6 EC
Semester 1, period 2
5334AQIT6Y
Quantum systems can be used to carry out a variety of tasks that are impossible in a classical world, e.g. entanglement-assisted super-dense coding. At the same time, the manipulation of quantum systems poses new challenges and requires new operational capabilities. For example, communicating over noisy quantum channels requires genuinely quantum encoding and decoding procedures, and entanglement needs to be refined and "distilled" before it becomes of any practical use.
Throughout the first part of the course, we will develop key mathematical tools such as trace inequalities and the variational characterisation of the the quantum relative entropy. We will see how the relative entropy emerges naturally from one of the simplest quantum tasks, hypothesis testing.
In the second part of the course, we will apply the above tools to pinpoint the ultimate performance enabled by quantum mechanics in communicating classical or quantum information over a noisy channel. We will also investigate the manipulation and distribution of entanglement between distant parties, an indispensable step to the construction of a quantum internet.
M. M. Wilde. Quantum Information Theory, 2nd Edition. Cambridge University Press, 2017. Available at https://arxiv.org/abs/1106.1445Links to an external site.. This very complete and didactic textbook is an excellent introduction to quantum Shannon theory.
J. Renes. Quantum Information Theory, Concepts and Methods. De Gruyter Oldenbourg, 2022. A modern textbook that takes a slightly different perspective from the one above.
M. Tomamichel. Quantum Information Processing with Finite Resources. SpringerBriefs in Mathematical Physics, 2016. Available at https://arxiv.org/abs/1504.00233Links to an external site.. Contains an excellent but agile discussion of quantum hypothesis testing and quantum relative entropies.
M. Hayashi. Quantum Information Theory: Mathematical Foundation, 2nd Edition. Springer Berlin Heidelberg, 2017. For the really curious and mathematically inclined among you, this is the reference textbook. It contains most of what you may ever want to know about quantum information.
R. Bhatia. Matrix Analysis. Springer New York, 2013. Great textbook on matrix analysis, especially if you are curious about the theory of operator monotone/concave functions.
T. M. Cover and J. A. Thomas. Elements of Information Theory. Wiley-Interscience, 2006. This excellent book is about classical information theory; it undermines several of the concepts we are going to explore in the quantum case, but is not strictly needed.
Some lecture notes will be made available at https://canvas.uva.nl/courses/39428/modules
Activity | Hours | |
Self study | 168 | |
Total | 168 | (6 EC x 28 uur) |
This programme does not have requirements concerning attendance (TER-B).
Additional requirements for this course:
Attendance is not mandatory.
| Item and weight | Details |
|
Final grade | |
|
0.6 (60%) Tentamen | |
|
0.4 (40%) Homeworks (best 6 out of 7) |
In case you choose to go for the resit, the homework grade will not count any more towards the final grade. That means that 100% of the final grade will consist of the resit grade.
Get in touch with Filippo Girardi at f.girardi@uva.nl
Each week before Friday I will upload an exercise sheet in the Modules section. You are supposed to mail the solution to Filippo Girardi (f.girardi@uva.nl) before the following Friday. Filippo will grade the sheets and assign a mark to each of them. The course lasts 7 weeks, so there will be 7 assignments. The final grade will consist of a 40% determined by averaging your best 6 scores out of 7 assignments, and the remaining 60% determined by the score of the final exam.
- Assignment 1, published Friday 03/11, due Friday 10/11
- Assignment 2, published Friday 10/11, due Friday 17/11
- Assignment 3, published Friday 17/11, due Friday 24/11
- Assignment 4, published Friday 24/11, due Friday 01/12
- Assignment 5, published Friday 01/12, due Friday 08/12
- Assignment 6, published Friday 08/12, due Friday 15/12
- Assignment 7, published Friday 15/12, due Friday 29/12
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
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