Graphical rule of transforming continuous-variable graph states by local homodyne detection
Jing Zhang · Physical Review A · 2010
Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules---local complement operation and vertex deletion (single quadrature-amplitude $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$ measurement)---the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.