Offer description: The Mathematical Institute of SAS in Bratislava offers a PhD position for research in quantum information theory, under supervision of Anna Jenčová http://www.mat.savba.sk/~jencova/index.html. The study is organized in cooperation with the Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava. Possible topics are the following:
- Relative entropies in quantum information theory.
Relative entropy is one of the fundamental concepts in information theory. These quantities describe operational characteristics of optimal procedures in various types of information-theoretic tasks, but also serve as an important mathematical tool. The class of quantum relative entropies is much richer than the classical counterpart and many of the possible quantities, their interpretations and mutual relations are not fully investigated. We focus on various versions of quantum Rényi relative entropies and their extensions, such as to infinite dimensions or for quantum channels, as well as their possible operational interpretations.
- Quantum channels and higher order maps
Quantum channels describe most general physically allowed transformations between quantum systems. The framework of higher order maps (HOMs) allows a more detailed study of general quantum protocols, such as channel measurements, channel transformations, channels with memory, etc. Nowadays there is an increasing interest in understanding the structure and properties of HOMs. Possible goals of the proposed thesis include the study of the mathematical structure of HOMs from different points of view, like operator theory, category theory, linear algebra or convex geometry. We will focus on nonclassical properties of HOMs, e.g. incompatibility or indefinite causal order, their classification, consequences and possible advantages in information processing.
The position requires a MSc. degree or equivalent in mathematics, or physics, but a good background in mathematics is necessary.
For more information, see https://musavsrv.mat.savba.sk/phdstudy.htm and https://fmph.uniba.sk/en/admissions/admissions-process/doctoral-degree-a...
Application requirements: Interested applicants should send the following materials to anna.jencova@mat.savba.sk:
- a CV including a list of publications (if any), with emphasis on the scientific results of the applicant
- motivation letter
- two academic recommendation letters (should be sent directly by the recommending person)
Further documents will be requested from selected candidates. The deadline for application submission is CET 23:59, April 20, 2025.
