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Graphical rule, describing that any single-mode homodyne detection turns agiven continuous-variable (CV) graph state into a new one, is presented.Employing two simple graphical rules: local complement operation and vertexdeletion (single quadrature-amplitude $\hat{x}$ measurement), the graphicalrule for any single-mode quadrature component measurement can be obtained. Theshape of CV weighted graph state may be designed and constructed easily from agiven larger graph state by applying this graphical rule.

Graphical rule of transforming continuous-variable graph states by local homodyne detection