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Quaternion Representation and Symplectic Spin Tomography

Journal of Russian Laser Research volume 34, pages 477–487 (2013)Cite this 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.

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Authors and Affiliations

  1. Russian Quantum Center, Novaya Str. 100, Skolkovo, Moscow Region, 143025, Russia

    Aleksey K. Fedorov

  2. Bauman Moscow State Technical University, The 2nd Baumanskaya Str. 5, Moscow, 105005, Russia

    Aleksey K. Fedorov & Evgeny O. Kiktenko

  3. Geoelectromagnetic Research Centre of Schmidt Institute of Physics of the Earth, The Russian Academy of Sciences, Troitsk, P.O. 30, Moscow Region, 142190, Russia

    Evgeny O. Kiktenko

Authors
  1. Aleksey K. Fedorov
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  2. Evgeny O. Kiktenko
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Correspondence to Aleksey K. Fedorov.

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Manuscript submitted by the authors in English on August 11, 2013.

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Fedorov, A.K., Kiktenko, E.O. Quaternion Representation and Symplectic Spin Tomography. J Russ Laser Res 34, 477–487 (2013). https://doi.org/10.1007/s10946-013-9378-z

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  • DOI: https://doi.org/10.1007/s10946-013-9378-z

Keywords

  • quantum tomography
  • spin tomograms
  • classical groups
  • quaternions