Linear optics and quantum maps

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.