We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the
two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.
We introduce a modification of the standard entanglement swapping protocol where the generation of entanglement between two distant modes is realized and verified using only local optical measurements. We show, indeed, that a simple condition on the
purity of the initial state involving also an ancillary mode is sufficient to guarantee the success of the protocol by local measurements {M. Abdi textit{et al.}, Phys. Rev. Lett. textbf{109}, 143601 (2012)}]. We apply the proposed protocol to a tripartite optomechanical system where the never interacting mechanical modes become entangled and certified using only local optical measurements.
We propose a protocol for entanglement swapping which involves tripartite systems. The generation of remote entanglement induced by the Bell measurement can be easily certified by additional local measurements. We illustrate the protocol in the case
of continuous variable systems where the certification is effective for an appropriate class of three-mode Gaussian states. We then apply the protocol to optomechanical systems, showing how mechanical entanglement between two remote micromechanical resonators can be generated and certified via local optical measurements.
