Graphs States and the necessity of Euler Decomposition Export

@article{citeulike:4009864, 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.}, archivePrefix = {arXiv}, author = {Duncan, Ross and Perdrix, Simon}, citeulike-article-id = {4009864}, citeulike-linkout-0 = {http://arxiv.org/abs/0902.0500}, citeulike-linkout-1 = {http://arxiv.org/pdf/0902.0500}, day = {3}, eprint = {0902.0500}, keywords = {category-theory, computation, graphs, logic, quantum-computation}, month = {Feb}, posted-at = {2009-02-05 01:14:15}, priority = {3}, title = {Graphs States and the necessity of Euler Decomposition}, url = {http://arxiv.org/abs/0902.0500}, year = {2009} }

TY - JOUR ID - citeulike:4009864 L3 - citeulike-article-id:4009864 N2 - 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. TI - Graphs States and the necessity of Euler Decomposition KW - category-theory KW - computation KW - graphs KW - logic KW - quantum-computation AU - Duncan, Ross AU - Perdrix, Simon PY - 2009/Feb/03/ UR - http://arxiv.org/abs/0902.0500 ER -