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J. Russian Laser Research, 2013, Volume 34, Issue 5, Pages 477–487 (Mi jrlr2)  

Quaternion representation and symplectic spin tomography

A. K. Fedorovab, E. O. Kiktenkocb

a Russian Quantum Center, Novaya Str. 100, Skolkovo, Moscow Region 143025, Russia
b Bauman Moscow State Technical University, The 2nd Baumanskaya Str. 5, Moscow 105005, Russia
c Geoelectromagnetic Research Centre of Schmidt Institute of Physics of the Earth, The Russian Academy of Sciences, Troitsk, P.O. 30, Moscow Region 142190, Russia

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.

Funding Agency Grant Number
Russian Quantum Center
Russian Foundation for Basic Research 12-05-00001
12-05-98009
Ministry of Education and Science of the Russian Federation SP-961.2013.5
A.K.F. is an RQC Fellow, and E.O.K. was supported by the Russian Foundation for Basic Research under Projects Nos. 12-05-0000 and 12-05-98009 and the Council for Grants of the President of the Russian Federation (Grant No. SP-961.2013.5).


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


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Document Type: Article
Received: 11.08.2013
Language: English

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