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)