Item

Abstract

We comprehensively review the quantum theory of the polarization properties
of light. In classical optics, these traits are characterized by the Stokes
parameters, which can be geometrically interpreted using the Poincaré sphere.
Remarkably, these Stokes parameters can also be applied to the quantum world,
but then important differences emerge: now, because fluctuations in the number
of photons are unavoidable, one is forced to work in the three-dimensional
Poincaré space that can be regarded as a set of nested spheres. Additionally,
higher-order moments of the Stokes variables might play a substantial role for
quantum states, which is not the case for most classical Gaussian states. This
brings about important differences between these two worlds that we review in
detail. In particular, the classical degree of polarization produces
unsatisfactory results in the quantum domain. We compare alternative quantum
degrees and put forth that they order various states differently. Finally,
intrinsically nonclassical states are explored and their potential applications
in quantum technologies are discussed.