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The local complementation rule is applied for continuous-variable (CV) graphstates in the paper, which is an elementary graph transformation rule andsuccessive application of which generates the orbit of any graph states. Thecorresponding local Gaussian transformations of local complementation forfour-mode unweighted graph states were found, which do not mirror the form ofthe local Clifford unitary of qubit exactly. This work is an important step tocharacterize the local Gaussian equivalence classes of CV graph states.

Local complementation rule for continuous-variable four-mode unweighted graph states