Publication: Extremal quantum states and their Majorana constellations
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2015-09-01
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Björk, G.
Klimov, Andrei B.
Hoz Iglesias, Pablo de la
Grassl, M.
Leuchs, Gerd
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American Physical Society
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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.
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©2015 American Physical Society. The authors acknowledge interesting discussions with Professor Daniel Braun and Olivia di Matteo. Financial support from the Swedish Research Council (VR) through its Linnaeus Center of Excellence ADOPT and Contract No. 621-2011-4575, the CONACyT (Grant No. 106525), the European Union FP7 (Grant Q-ESSENCE), and the Program UCM-Banco Santander (Grant No. GR3/14) is gratefully acknowledged. G.B. thanks the MPL for hosting him and the Wenner-Gren Foundation for economic support.
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