  Continuous-variable (CV) qubits can be created on an optical longitudinal
mode in which quantum information is encoded by the superposition of even and
odd Schroedinger's cat states with quadrature amplitude. Based on the analogous
features of paraxial optics and quantum mechanics, we propose a system to
generate and detect CV qubits on an optical transverse mode. As a
proof-of-principle experiment, we generate six CV qubit states and observe
their probability distributions in position and momentum space. This enabled us
to prepare a non-Gaussian initial state for CV quantum computing. Other
potential applications of the CV qubit include adiabatic control of a beam
profile, phase shift keying on transverse modes, and quantum cryptography using
CV qubit states.
