Oxford University Computing Laboratory
4pm Tuesday, 28th September, 2010
Room 4.31/33, Informatics Forum
While multipartite quantum states constitute a key resource for quantum computations and protocols, obtaining a high-level, structural understanding of entanglement involving arbitrarily many qubits is a long-standing open problem in quantum computer science. We approach this problem by identifying the close connection between a special class of highly entangled tripartite states, which we call Frobenius states, and the standard notion of a commutative Frobenius algebra. We use these states (and their induced algebra) as a primitive in a graphical language that is both universal for quantum computation and capable of highlighting the behavioural differences in types of Frobenius states. This graphical language then suggests methods for state preparation, classification, and efficient classical modeling of certain kinds of quantum systems.