Hannover 2016 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 10: Quantum Optics II
Q 10.2: Talk
Monday, February 29, 2016, 14:45–15:00, f442
Decoupling and invariants of one-dimensional symmetric quantum walks — Christopher Cedzich1, •Tobias Geib1, Francisco Alberto Grünbaum2, Christoph Stahl1, Luis Velazquez3, Albert Werner4, and Reinhard Werner1 — 1Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover — 2Department of Mathematics, University of California, Berkeley CA 94720 — 3Departamento de Matemática Aplicada & IUMA, Universidad de Zaragoza, María de Luna 3, 50018 Zaragoza, Spain — 4Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin
We study one-dimensional quantum walks satisfying a set of discrete symmetries and a gap condition. For most of the usual symmetry types, a classification can be built on decoupling, i.e., an arbitrary walk can be deformed continuously and while respecting symmetry and gap conditions into one consisting of two non-interacting half chains. The additional eigenvalues appearing after such decoupling are the basis of the classification. One symmetry type (namely DIII in the Cartan classification) does not seem to allow decoupling in general. For this type an alternative approach presented in a related talk by C. Cedzich can be applied.