  We experimentally demonstrate a controlled-phase gate for continuous
variables in a fully measurement-based fashion. In our scheme, the two
independent input states of the gate, encoded in two optical modes, are
teleported into a four-mode Gaussian cluster state. As a result, one of the
entanglement links present in the initial cluster state appears in the two
unmeasured output modes as the corresponding entangling gate acting on the
input states. The genuine quantum character of this gate becomes manifest and
is verified through the presence of entanglement at the output for a product
two-mode coherent input state. By combining our controlled-phase gate with the
recently reported module for universal single-mode Gaussian operations [R. Ukai
et al., Phys. Rev. Lett. 106, 240504 (2011)], it is possible to implement
universal Gaussian operations on arbitrary multi-mode quantum optical states in
form of a fully measurement-based one-way quantum computation.
