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Journal of Russian Laser Research

, Volume 34, Issue 5, pp 477–487 | Cite as

Quaternion Representation and Symplectic Spin Tomography

  • Aleksey K. FedorovEmail author
  • Evgeny O. Kiktenko
Article

Abstract

Quantum tomography for continuous variables is based on the symplectic transformation group acting in the phase space. A particular case of symplectic tomography is optical tomography related to the action of a special orthogonal group. In the tomographic description of spin states, the connection between special unitary and special orthogonal groups is used. We analyze the representation for spin tomography using the Cayley–Klein parameters and discuss an analog of symplectic tomography for discrete variables. We propose a representation for tomograms of discrete variables through quaternions and employ the qubit-state tomogram to illustrate the method elaborated.

Keywords

quantum tomography spin tomograms classical groups quaternions 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Russian Quantum CenterMoscow RegionRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia
  3. 3.Geoelectromagnetic Research Centre of Schmidt Institute of Physics of the EarthThe Russian Academy of SciencesMoscow RegionRussia

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