Inst. für Theoretische Physik

Topics for Bachelor and Master Theses

Below you find a suggestive list of topics for bachelor and master theses that are currently available in our group. If you are interested in any of them, or interested in general in writing a thesis in our group, just contact us!

Topics for Bachelor Theses

Quantum capacity bounds from positive maps

Maps that are positive but not completely positive can yield bounds on the capacity of quantum channels to transmit quantum information. The goal of this project is to evaluate such bounds that are based on the so-called diamond norm, and to investigate whether the obtained rates are actually strong converse rates for the quantum capacity, which means that they would limit the quantum capacity in an operationally strict sense. This is known to be so for the upper bound coming from the transposition map, but unknown for other positive maps. On the other hand, the verity of a certain conjectured inequality for the diamond norm under the transposition map would yield a new proof of the strong converse property. The project will lead to familiarity with essential notions of Quantum Information Theory and in particular with semidefinite programming - both its theory and its computational implementation.

Contact Person: Dr. David Reeb

Uncertainty relations

The joint numerical range of local measurements.

Contact Person: Rene Schwonnek

Quantum communication

Entanglement distillation by stochastic protocols respecting the positivity of the partial transpose.

Contact Person: Rene Schwonnek

Topological quantum error-correcting codes

Topologically ordered systems can be used to store quantum information in a naturally fault-tolerant way. The scope of this project would be to investigate different codes and their properties, as well as to implement a numerical simulation of such an error-correcting code and to test it against different models of noise.

Contact Person: Marius Lewerenz

Quantum universal and classically simulable gate sets

Quantum computers are modelled by quantum circuits consisting of certain elementary operations, so-called quantum gates. Several gate sets have been proven to be universal for quantum computation. On the other hand, gate sets that can be simulated by classical computers are also known to exist. What criterions do they have to fulfill? And do there exist gate sets that are of neither kind, i.e. that are capable of a computational power between classical and quantum?

Contact Person: Friederike Dziemba

Topics for Master Theses

Improvements of the data processing inequality

The data processing inequality for quantum operations - in the form of either the famous “strong subadditivity property of quantum entropy” or the “monotonicity of the quantum relative entropy” - is a basic tenet for many application in quantum information theory. The data processing inequality has recently been improved in a quantitative manner, and it has also been shown to hold for quantum operations that are merely positive. One goal of this project is to investigate whether these two results can be combined: Do the similar improvements of the data processing inequality hold for general positive evolutions? And how can one apply these results to improve other entropy inequalities such as the concavity of the von Neumann entropy? This project will involve many cental notions from Quantum Information and Shannon Theory, but also complex analysis and interpolation theory which are central to proofs of the data processing inequality.

Contact Person: Dr. David Reeb

Last modified: 24 January 2017
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