Continuous-variable experiments with optical qubits

We present experimental homodyne tomography of an optical quantum bit represented by a single photon split into two optical modes. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical qubit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments. We also show that a homodyne measurement on just one of the modes leads to remote preparation of a single-rail optical qubit in the other mode.