We present a scheme for the preparation of one-dimensional （1D） and two-dimensional （2D） cluster states with electrons trapped on a liquid helium surface and driven by a classical laser beam. The two lowest levels of the vertical motion of the electron act as a two-level system, and the quantized vibration of the electron along one of the parallel directions （the x direction） serves as the bosonic mode. The degrees of freedom of the vertical and parallel motions of the trapped electron can be coupled together by a classical laser field. With the proper frequency of the laser field, the cluster states can be realized.
We propose a scheme for long-distance quantum state transfer between different atoms based on cavity-assisted interactions. In our scheme, a coherent optical pulse sequentially interacts with two distant atoms trapped in separated cavities. Through the measurement of the state of the first atom and the homodyne detection of the final output coherent light, the quantum state can be transferred into the second atom with a success probability of unity and a fidelity of unity. In addition, our scheme neither requires the high-Q cavity working in the strong coupling regime nor employs the single-photon quantum channel, which greatly relaxes the experimental requirements.
We propose a scheme for generating a genuine four-particle polarisation entangled state ｜χ^00） that has many interesting entanglement properties and potential applications in quantum information processing. In our scheme, we use the weak cross-Kerr nonlinear interaction between field-modes and the non-demolition measurement method based on highly efficient homodyne detection, which is feasible under the current experiment conditions.
