Towards Normal Forms for GHZ/W Calculus

Details Towards Normal Forms for GHZ/W Calculus Towards Normal Forms for GHZ/W Calculus

2011-04-13

arxiv.org/abs/1104.2480v1

AIP Conf. Proc. 1384, 112-119 (2011)

Computer Science

Logic in Computer Science

8 pages. AIP format. To appear in AIP proceedings of the International Symposium on "75 Years of Quantum Entanglement: Foundat

Scientific paper

10.1063/1.3635852

Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express arbitrary mutlipartite quantum states equivalent under stochastic local operations and classical communication (SLOCC). However, it is still not clear how to explicitly identify which graphical properties lead to what states. This can be achieved if we have well-behaved normal forms for arbitrary graphs within this calculus. This article lays down a first attempt at realizing such normal forms for a restricted class of such graphs, namely simple and regular graphs. These results should pave the way for the most general cases as part of future work.

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