Graphs States and the necessity of Euler Decomposition

Details Graphs States and the necessity of Euler Decomposition Graphs States and the necessity of Euler Decomposition

2009-02-03

arxiv.org/abs/0902.0500v1

Physics

Quantum Physics

15pages, 38 figures

Scientific paper

Coecke and Duncan recently introduced a categorical formalisation of the interaction of complementary quantum observables. In this paper we use their diagrammatic language to study graph states, a computationally interesting class of quantum states. We give a graphical proof of the fixpoint property of graph states. We then introduce a new equation, for the Euler decomposition of the Hadamard gate, and demonstrate that Van den Nest's theorem--locally equivalent graphs represent the same entanglement--is equivalent to this new axiom. Finally we prove that the Euler decomposition equation is not derivable from the existing axioms.

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