Continuous-variable Gaussian analog of cluster states

We present a continuous-variable (CV) Gaussian analog of cluster states, a new class of CV multipartite entangled states that can be generated from squeezing and quantum nondemolition coupling $H_I=\hslash \chi X_A{X}_B$. The entanglement properties of these states are studied in terms of classical communication and local operations. The graph states as general forms of the cluster states are presented. A chain for a one-dimensional example of cluster states can be readily experimentally produced only with squeezed light and beam splitters.