Date: 12 September 2014, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: David Lyons, Lebanon Valley College
   Title: Graphs and Hypergraphs, Symmetry and Entanglement

Abstract.  In the long list of applications of the
spectacularly simple but effective notion of a graph is the quantum graph
state: each vertex corresponds to a quantum bit, and each edge defines an
entangling operator. Graph states in turn show up in a range of
applications as resources for quantum computation and coding
schemes. Hypergraphs generalize graphs by allowing arbitrary sets of
vertices to be hyperedges, and quantum hypergraphs are defined using a
natural generalization to hyperedges of the edge operator. We present
recent work that extends to hypergraph states some of the well-developed
theory of graph states. In particular, we give recent results on local
unitary symmetries and make connections with entanglement properties.