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2009

Graphs States and the necessity of Euler Decomposition

Duncan, Ross, Perdrix, Simon

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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.

Graphs States and the necessity of Euler Decomposition · Around

Built on

Coherence for compact closed categories
Kelly, G., Laplaza, M.: · 1980
Earlier work this paper cites.
The geometry of tensor categories i
Joyal, A., Street, R.: · 1991
Earlier work this paper cites.
A one-way quantum computer
Raussendorf, R., Briegel, H.J.: · 2001
Earlier work this paper cites.
A categorical semantics of quantum protocols
Abramsky, S., Coecke, B.: · 2004
Earlier work this paper cites.

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