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Graphical description of the action of local Clifford transformations on graph states

Maarten Van den Nest·Jeroen Dehaene·Bart De Moor
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Abstract

We translate the action of local Clifford operations on graph states into transformations on their associated graphs - i.e. we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the evolution of graph states under local Clifford operations. As we will show, there is essentially one basic rule, successive application of which generates the orbit of any graph state under local unitary operations within the Clifford group.

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Maarten Van den Nest, Jeroen Dehaene, Bart De Moor. 2004-02-17. Graphical description of the action of local Clifford transformations on graph states. https://doi.org/10.1103/physreva.69.022316

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