**Optical qubit: a continuous-variable approach**

We use homodyne tomography to characterize a dual-rail optical qubit as a state of the electromagnetic field
in a pair of optical modes. From correlated, phase-sensitive field quadrature statistics acquired from two
homodyne detectors, we reconstruct the four-dimensional density matrix which extends over the entire
Hilbert space of two electromagnetic oscillators and reveals, for the first time, complete information about
the optical qubit, including the vacuum and multiphoton contributions. Furthermore, the continuous-variable
experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon
counting experiments [1]. The dual-rail optical qubit can be viewed as an entangled ensemble of the singlephoton
and vacuum states and can be used as a resource for quantum teleportation [2] and remote state
preparation [3] in a hybridized discrete- and continuous-variable regime. More generally, our experiments
demonstrate the potential of combining discrete- and continuous-variable approaches in a single setting for
quantum information processing applications.
[1] S. A. Babichev, J. Appel, A. I. Lvovsky, Phys. Rev. Lett. 92, 193601 (2004)
[2] S. A. Babichev, J. Ries, A. I. Lvovsky, Europhys. Lett. 64, 1 (2003)
[3] S. A. Babichev, B. Brezger, A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004)