@inproceedings{Duncan:2009ph,
  abstract = "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.",
  author = "Ross Duncan and Simon Perdrix",
  booktitle = "Computability in Europe: Mathematical Theory and Computational Practice (CiE'09)",
  doi = "10.1007/978-3-642-03073-4",
  editor = "Ambos-Spies, K. and L\"{o}we, B. and Merkle, W.",
  keywords = "quantum computing; categorical quantum mechanics; graphical calculi; measurement-based quantum computing; entanglement",
  note = "Preprint available at http://arxiv.org/abs/0902.0500",
  pages = "167--177",
  publisher = "Springer",
  series = "Lecture Notes in Computer Science",
  title = "Graph States and the necessity of Euler Decomposition",
  volume = "5635",
  year = "2009",
}