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- Björk, Gunnar, et al.
(author)
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Stars of the quantum Universe : extremal constellations on the Poincare sphere
- 2015
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In: Physica Scripta. - : IOP Publishing. - 0031-8949 .- 1402-4896. ; 90:10
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Journal article (peer-reviewed)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.
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| 3. |
- Goldberg, Aaron Z., et al.
(author)
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Quantum concepts in optical polarization
- 2021
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In: Advances in Optics and Photonics. - : The Optical Society. - 1943-8206. ; 13:1, s. 1-73
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Research review (peer-reviewed)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 Poincare 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 Poincare 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.
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