The project focuses on finite geometries (in particular geometries over rings) and their role as a link and unifying platform between at first sight rather different domains of physics and chemistry.
Quantum information theory:
Here we focus our attention at two goals: On the one hand, we aim at extending our finite-ring-geometrical theory of the generalized Pauli group of a single qudit to the case of multiple qudits. On the other hand, we plan to ascertain which geometrical and combinatorial aspects of a projective ring geometry directly relate to entanglement in a given quantum system, and to which extent these entities can provide a quantitative measure for entanglement.
Chemistry of coupling:
We intend to put forward first rudimentary discrete models of chemical bonds that are fully devoid of divergences and degenerations exhibited by continuous models. As a subsequent step, we plan to explore the finest traits of hierarchical properties of chemically bonded systems, with a particular focus on a gradual disappearance of the boundary between individual building blocks, and, hence, of the dichotomy 'the object and its surroundings'.
Stringy black holes:
We would like to inspect which finite geometries underlie the (already known and yet to be unveiled) relations between black-hole entropies and entanglement invariants characterizing multi-qubit/qudit systems. A particular attention will be paid to the role of the Fano plane and its recently discovered non-unimodular 'Snowflake' generalizations, generalized polygons of small order, and biplanes of small order.
The main outcome of the project should be:
Fellows of the Cooperation Group:
Andrea Blunck (Hamburg), Péter Lévay (Budapest), Michel Planat (Besançon), Petr Pracna (Prag)
Andrea Sanigová (Tatranská Lomnica), Michael Duff (Imperial College London, United Kingdom), Thomas Honold (Hangzhou, China), Alexander Kreuzer (University of Hamburg), Apostol Vourdas (University of Bradford, United Kingdom)