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

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.

8 pages, 1 figure. Former title: "The evolution of graph states under local Clifford operations as graph transformations". Replaced with revised version. Minor changes. To appear in Phys. Rev. A

References in corpus (5)

• Measurement-based quantum computation with cluster states
• Quantum Error Correction and Orthogonal Geometry
• Multiparticle entanglement purification for graph states
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Local permutations of products of Bell states and entanglement distillation

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