University of Oxford Logo University of OxfordDepartment of Computer Science - Home
On Facebook
Facebook
Follow us on twitter
Twitter
Linked in
Linked in
Flickr
Flickr
Google plus
Google plus
Digg
Digg
Pinterest
Pinterest
Stumble Upon
Stumble Upon

Oxford Quantum Talks Archive

Entanglement classification with classical structures and graph rewriting

Aleks Kissinger, Oxford University
Categories, Logic and Foundations of Physics V, August 2009, Imperial College London

Graphical languages have proven a powerful tool for reasoning about arrows in various kinds of monoidal categories, and in particular about quantum states and processes. We review a graphical language that exploits the relationships between simple maps on mutually unbiased bases. This is the language of complementary classical structures, or the "red-green" calculus. We show how this language can encode many multipartite entangled states, and how the behaviour of these states is emergent as the result of graph rewriting. However, manual manipulation of medium to large graphs quickly becomes difficult and error-prone. Worse still, the expansion of the red-green theory in light of relationships discovered in the underlying (e.g. qubit) semantics requires arduous translations between graphical and matrix representations of quantum states. To combat these issues, we introduce Quantomatic, a program that allows automated and semi-automated explorations of graph rewrite systems. It also interfaces with a computer algebra system to do concrete calculations on the underlying semantics of a graph. In this talk, we shall demonstrate how Quantomatic uses rewriting and computer algebra to probe and help classify multipartite entangled states.

[video] [streaming video]