König Group

Our research centers around operational problems related to the storage, manipulation and transmission of quantum information. Through our work, we wish to elucidate the exact potential of quantum systems when used as an information-processing resource.

Quantum fault-tolerance and many-body physics:

Many-body systems such as interacting spin lattices offer an attractive substrate for robust information processing. We are interested in explicit schemes, as well as fundamental limitations on quantum memories and fault-tolerant gates relying on collective degrees of freedom. We aim to develop tools for assessing the merits of non- standard approaches towards enhancing protocols, such as the use of Anderson localization in  memories.

Finding suitable mechanisms for preparation, as well as readout of encoded information represents an interesting theoretical challenge. More generally, we focus on questions of interconvertibility of different states by a given set of operations (such as those experimentally available); these are related to the fundamental problem of classifying different phases of matter.

Selected publications:

- R. König and S. Bravyi. Classification of topologically protected gates for local stabilizer Physical Review Letters, vol. 110, no. 170503, April 2013.
- J. Dengis, R. König and F. Pastawski. An optimal dissipative encoder for the toric code. New Journal of Physics, 16, 013023, October 2013.
- S. Bravyi and R. König. Disorder-assisted error correction in Majorana chains. Communications in Mathematical Physics, vol. 361, pp. 641–692, October 2012.
- R. König, G. Kuperberg and B. Reichardt. Quantum computation with Turaev-Viro codes. Annals of Physics, vol. 325, no. 12, pp. 2707–2749, December 2010.

Quantum information and communication:

Basic tenets of classical information theory need to be reevaluated and often significantly revised in the presence of quantum effects. A major goal is to identify suitable information measures in a quantum setting, and to establish corresponding mathematical properties. This research is driven by the desire to make quantitative statements in scenarios arising in quantum communication and cryptography. More recently, our focus has been on communication over bosonic quantum channels, including cases where non-Gaussian noise is present.

Selected publications:

- R.König and G.Smith. Limits on classical communication from quantum entropy power inequalities. Nature Photonics, vol. 7, pp. 140–146, January 2012.
- R. König, S. Wehner and J. Wullschleger. Unconditional security from noisy quantum storage. IEEE Transactions on Information Theory, vol. 58, no. 3, pp. 1962- 1984, March 2012.
- R. König and S. Wehner. A strong converse for classical channel coding using entangled inputs. Phys. Rev. Lett. 103, 070504, August 2009.
- R. König, R. Renner and C. Schaffner. The operational meaning of min- and max-entropy. IEEE Transactions on Information Theory, vol. 55, no. 9, pp. 4337-4347, September 2009.

Variational quantum physics and simulation:

The operational viewpoint on physical systems has benefitted the development and analysis of variational methods, essentially providing a conceptual framework and a language for quantifying quantum correlations. We aim to further exploit these fruitful interactions, connecting e.g., state preparation protocols to the entanglement structure of many-body states. Of particular interest are statements about the accuracy of a given method. We aim to establish such error bounds by exploiting underlying symmetries. This involves the application of representation-theoretic methods to e.g., tensor network states.

Selected publications:

• R. König and E. Bilgin. Anyonic entanglement renormalization. Phys. Rev. B 82, 125118, September 2010.
• R. König, B. Reichardt and G. Vidal. Exact entanglement renormalization for string-net models. Phys. Rev. B 79, 195123, May 2009.
• M. Christandl, R. König, G. Mitchison and R. Renner. One and a half quantum de Finetti theorems. Comm. Math. Phys., 273 (2), 473–498, 2, July 2007.

Prof. Robert König


Zentrum Mathematik TUM, M5
Technische Universität München
Boltzmannstrasse 3
85748 Garching

Büro:         03.12.039
Tel.:         +49 89 289-17042
E-Mail:         robert.koenigemattum.de

Group webpage