  The orbital angular momentum of light, unlike spin, is an
infinite-dimensional discrete variable and may hence offer enhanced
performances for encoding, transmitting, and processing information in the
quantum regime. Hitherto, this degree of freedom of light has been studied
mainly in the context of quantum states with definite number of photons. On the
other hand, field-quadrature continuous-variable quantum states of light allow
implementing many important quantum protocols not accessible with photon-number
states. Here, we present the first generation and complete experimental
characterization of a bipartite continuous-variable Gaussian entangled state
endowed with non-zero orbital angular momentum. A q-plate is used to transfer
the continuous-variable entanglement initially generated in polarization into
orbital angular momentum. We then apply a reconfigurable homodyne detector to
various combinations of orbital angular momentum modes in order to reconstruct
the entire quantum-state covariance matrix, by directly measuring the
fluctuations of quadrature operators. Our work is a step towards generating
multipartite continuous-variable entanglement in a single optical beam.
