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