Stars of the quantum Universe : extremal constellations on the Poincare sphere

• The characterization of the polarization properties of a quantum state requires the knowledge of the joint probability distribution of the Stokes variables. This amounts to assessing all the moments of these variables, which are aptly encoded in a multipole expansion of the density matrix. The cumulative distribution of these multipoles encapsulates in a handy manner the polarization content of the state. We work out the extremal states for that distribution, finding that SU(2) coherent states are maximal to any order, so they are the most polarized allowed by quantum theory. The converse case of pure states minimizing that distribution, which can be seen as the most quantum ones, is investigated for a diverse range of number of photons. Exploiting the Majorana representation, the problem appears to be closely related to distributing a number of points uniformly over the surface of the Poincare sphere.

Subject headings

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

polarization

quantum optics

fluctuations

anti-coherence

Majorana representation

spherical t-design

Publication and Content Type

ref (subject category)

art (subject category)