Workshop on

Quantum Mechanics: Axiomatics of Measurements and connections with Computing and Information Retrieval

On the structure of Clifford quantum cellular automata

aula DOTTORATO - MARTEDì 12 DICEMBRE ore 10.00
  DIRK SCHLINGEMANN, Technical University of Braunschweig

1987-1996: Study in Physics at the University of Hamburg (Germany), Diploma and PhD in the field of "algebraic quantum field theory" at the II. Institute for Theoretical Physics in the group of Klaus Fredenhagen.
1997-1999: Research project in quantum field theory an euclidean field theory at the Erwin Schrödinger International Institute for Mathematical Physics (ESI), Vienna associated with the group of Jakob Yngvason at the Institut für Theoretische Physik, University Vienna. Funding by the DFG, the ESI and the Jubiläumsfonds der Oesterreichischen Nationalbank.
Since 2000: Research associate at the Institut für Mathematische Physik, Technical University Braunschweig, in the quantum information theory research group of Reinhard Werner. Funding by the DFG and EQUIP.

  A reversible quantum cellular automata is an invertible quantum channel that acts on a countable set single cell systems arranged by a lattice. The automaton commute with the lattice translations and its restriction to a single cell only depends on the next neighbor cells. The talk is concerned with a special subclass of quantum cellular automata, the so called "Clifford quantum cellular automata". The system of each single cell can be described in terms of "discrete Weyl (displacement) operators" corresponding to translations in discrete phase space. Clifford quantum cellular automata assign to Weyl operators multiples of Weyl operators which implies that they are induced by symplectic transformations. It is discussed how to obtain a structural as well as a constructive characterization of all Clifford quantum cellular automata.