Abstract
We present protocols for remote implementation of general operators between two nodes, which are considered: the first where an arbitrary single-qubit operation acts on photon state in the polarization degree of freedom, and the second with photon state in the temporal degree of freedom. By employing simultaneous entanglement in two independent degrees of freedom, both protocols are fulfilled near deterministically in two steps. In the first step, the effective cross-Kerr interaction and X-quadrature measurements of the coherent states are main tools for achieving the goal. Together with the available existing optical elements and common single-photon detectors, the construction circuit of the second step is simple and feasible with current technologies. Our protocols are beneficial to long-distance quantum communication and quantum metrology.
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