We present an experimental study of the non-classical correlations of a pair
of spatial qubits formed by passing two down-converted photons through a pair
of double slits. After confirming the entanglement generated in our setup by
quantum tomography using separate measurements of the slit images and the
interference patterns, we show that the complete Hilbert space of the spatial
qubits can be accessed by measurements performed in a single plane between the
image plane and the focal plane of a lens. Specifically, it is possible to
obtain both the which-path and the interference information needed for quantum
tomography in a single scan of the transversal distribution of photon
coincidences. Since this method can easily be extended to multi-dimensional
systems, it may be a valuable tool in the application of spatial qudits to
quantum information processes.Comment: 19 pages, including 10 figures and 2 table
