Extremal quantum states and their Majorana constellations

TL;DR

This paper investigates extremal quantum states in polarization, identifying maximal SU(2) coherent states and exploring minimal states through Majorana representations, revealing their geometric distribution on the Poincare sphere.

Contribution

It introduces a novel analysis of extremal quantum polarization states using Majorana constellations, highlighting the geometric distribution of minimal states.

Findings

SU(2) coherent states are maximal at all orders

Minimal states are characterized by uniform point distributions on the Poincare sphere

Majorana representation provides a geometric perspective on quantum polarization states

Abstract

The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those multipoles and work out the corresponding extremal pure states. We find that SU(2) coherent states are maximal to any order whereas the converse case of minimal states (which can be seen as the most quantum ones) is investigated for a diverse range of the number of photons. Taking advantage of the Majorana representation, we recast the problem as that of distributing a number of points uniformly over the surface of the Poincare sphere.