**Continuous-variable experiments with a nonlocal single photon **

A two-mode optical qubit is generated when a single photon from a parametric down conversion source entangles itself with a vacuum on a beam splitter. We have characterized this dual-rail state by means of homodyne tomography. From the quadrature statistics, applying the maximum likelihood method, density matrix is calculated which extends over the entire Hilbert space and thus reveals, for the first time, complete information about the qubit as a state of the electromagnetic field. A nonlocal nature of the reconstructed state is shown by a violation of the Bell inequality for the experimental data converted to a dichotomic format. This experiment can be interpreted as remote preparation of an arbitrary single-mode optical qubit. By measuring a quadrature on one of the spatial modes of the entangled state, we project the other mode onto a coherent superposition of the single-photon and vacuum states. Surprisingly, the state obtained in this manner can be of higher purity than the single-photon resource we started with.