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Journal Article

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

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Grassl,  Markus
Optics Theory Group, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Leuchs,  Gerd
Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Sanchez-Soto,  Luis L.
Guests, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Bjork, G., Grassl, M., de la Hoz, P., Leuchs, G., & Sanchez-Soto, L. L. (2015). Stars of the quantum Universe: extremal constellations on the Poincare sphere. PHYSICA SCRIPTA, 90(10): 108008. doi:10.1088/0031-8949/90/10/108008.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-636A-E
Abstract
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.