Mathematical Institute
Topic
Quantum channels and higher order maps
PhD. program
9-1-9 Applied mathematics
Name of the supervisor
Mgr. Anna Jenčová, DrSc.
Contact:
Receiving school
Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava
Annotation
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.