# Classical and Quantum Theory of Information (Shannon Theory)

## Lecture details

__Please note that the lecture listed in the RWTH online information for courses by M. Wegewijs is currently not correct. The following lecture is the correct one: __

The lecture will be given by Professor Wegewijs.

**Description:**

The aim of this course is to work through the text on "Quantum Shannon theory" in Chapter 10 of "Quantum information" by J. Preskill (Ref.: https://arxiv.org/pdf/1604.07450.pdf). More background is provided in the extensive book "Quantum Information Theory" by M. Wilde (Ref.: http://www.markwilde.com/qit-notes.pdf).

These present a host of fairly recent results which are also of interest to students interested areas other than quantum information theory, such as open quantum systems and quantum thermodynamics.

Points of interest:

- What do various entropies and related information measures concretely quantify in physical quantum circuits ('operational approach')? Which of these quantities can never decrease and why?

- What is the difference between classical and quantum information due to indistinguishability of quantum states and entanglement between different quantum systems? Why can quantum conditional entropy be negative?

- Under which condition can the effect of the environment on a quantum state be 'reversed' (thermodynamics) or 'decoded' (quantum error correction)?

- The presented approach applies to general open quantum systems without simplifying approximations that are often made in traditional statistical physics (weak coupling, Markov approximation, etc.).

The required background in quantum-information theory will be provided within the course and is minimal (density operators, POVM measurements, quantum channels, Kraus operators). Other QI courses are complementary and their attendance is useful but not necessary.

**Contents:**

- Entropy, conditional entropy, relative entropy, mutual information, coherent information, accessible information and Holevo bound; their relations and inequalities

- Information compression, distributed compression

- Entanglement measures: entanglement cost, distillable entanglement, squashed entanglement

- Communication, entanglement-assisted communication, channel capacities

- Quantum resource theory and inequalities, fundamental communication protocols, decoupling principle and random coding

At the end of the semester research papers should be presented, possible topics including:

- Markov-chain quantum states: quantum conditional mutual information

- Markov quantum evolutions: CP-divisible evolution, time-dependent Lindblad theory

- Quantum thermodynamics: entropy production, converting entanglement into work, Maxwell daemons

- Quantum-information measures in many-body methods: entanglement in DMRG, MPS, PEPS

- Quantum error correction: decoding conditions

Suggestions for topics that interest the participants are encouraged but should, of course, be agree upon during the semester.

Time | Room | Start/Finish |
---|---|---|

Fri 12.30pm -2.45pm (The lecture times can be adjusted to suit the needs of the participants.) |
4273 (MBP2 116) | 12.10.2018 - 01.02.2019 |