Workshop on

Quantum Measurements and Operations for Criptography and Information Processing

On quantum information processing with graph states

aula DOTTORATO - MERCOLedì 12 OTTOBRE ore 15.00
  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.

Dirk Schlingemann
  Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Rau{\ss}endorf as a resource for a new model of {\em one-way quantum computing}, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed in our research group, as a tool to build quantum error correcting codes, called {\em graph codes}. The connection between the two approaches was fully realized in close cooperation. The talk provides a survey of the theory of graph states. The theoretical and mathematical background for the analysis of graph states and one-way quantum computing is presented. In particular, the implementation of quantum error correcting codes is described. In addition to that, interaction processes are discussed, which enable the creation of graph states on very large systems. Graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, a constructive characterization of translationally invariant graph states is given.