Ulm 2004 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 4: Quanteninformationstheorie

MP 4.4: Fachvortrag

Dienstag, 16. März 2004, 15:15–15:40, H 21

Quasi-free quantum cellular automata — •Dirk Schlingemann — Institut für Mathematische Physik, TU-Braunschweig

The concept of a quantum cellular automaton (QCA) is introduced from an C*-algebraic point of view. The observable algebra of the underlying system is modeled the tensor product of a finite dimensional matrix algebra over an infinitely extended regular lattice. A QCA is given by an automorphism which commutes with the spatial translations and which maps the algebra at a given position into the tensor product of next neighbors (local transition rule). We are concerned with a particular class of QCA which we call No-dqquasi-free QCANo-dq: The matrix algebra at each position of the lattice is generated by a discrete Weyl system, i.e. an irreducible unitary projective representation of a finite abelian group. This group is interpreted as classical discrete phase space. Quasi-free QCAs map No-dqWeyl operatorsNo-dq (unitary representatives) onto multiples of Weyl operators. They are therefore induced by canonical transformations on the corresponding discrete phase space. We discuss the structure of quasi-free QCA by characterizing those canonical transformations which lead to a well defined automata.