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The Bialynicki-Birula-Sipe photon wave function formalism is extended to include the interaction between photons and continuous non-absorptive media. When the second quantization of this formalism is introduced, a new method for describing the quantum interactions between light and matter emerges. As an example of the application of the method, an expression for the quantum state of the twin photons generated by parametric downconversion is derived in agreement with previous treatments, but with a more intuitive interpretation. [ABSTRACT FROM AUTHOR]

We report an experiment to generate and propagate two entangled spatial qudits, $\mathcal{D}$-dimensional quantum systems, using spontaneous parametric down-conversion. The manipulation, via pump beam, of the transverse spatial correlation between the photon pairs is explored. Inserting apertures with $\mathcal{D}$-slits in the arms of the down-converted photons, we associate the qudit space with the $\mathcal{D}$ possible paths followed by each photon. Experimental results for qudits with $\mathcal{D} = 4$ and 8 are shown. We demonstrate that the generated states cannot be classically correlated. We also show the propagation of entangled states of spatial qudits. Their free-space distribution is performed at the laboratory scale and the propagated states maintain a high fidelity with their original form. [ABSTRACT FROM AUTHOR]

We discuss how it is possible to manipulate quantum spatial properties of light beams by using the transfer of the angular spectrum. Twin beams from the parametric down-conversion can be prepared in a state that carries two different quantum images. At the same time, the twin photons can be entangled in polarization. This preparation allows the selection between the detection of each one of the images at a time or a mixture by performing proper projections onto polarization sub-spaces. As another example, we show how to produce a light beam presenting spatial anti-bunching through the control of the entangled angular spectrum and reflections. [ABSTRACT FROM AUTHOR]