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Quantum Tomography of Wigner Functions from Incomplete Data

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International Trends in Optics and Photonics

Part of the book series: Springer Series in OPTICAL SCIENCES ((SSOS,volume 74))

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Summary

In this chapter we will study how the states of light can be reconstructed from the knowledge of a restricted set of mean values of system observables. We will show how the maximum entropy (MaxEnt) principle can be applied for a reconstruction of quantum states of light fields. The chapter is organized as follows. In Sect. 2 we briefly describe the main ideas of the MaxEnt principle. In Sect. 3 we set a scene for a description of the reconstruction of quantum states of light fields. In this section we briefly discuss the phase-space formalism which can be used for a description of quantum states of light. In Sect. 4 we introduce various observation levels suitable for a description of light fields and we present the reconstruction of Wigner functions of these fields prepared in nonclassical states. Finally, in Sect. 5 we present the results of the numerical reconstruction of quantum states of light from incomplete tomographic data. We compare two reconstruction schemes: reconstruction via the MaxEnt principle and reconstruction via direct sampling (i.e. the tomography reconstruction via pattern functions — see below in Sect. 3).

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Authors
  1. V. Bužek
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  2. G. Drobný
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  3. H. Wiedemann
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Editor information

Editors and Affiliations

  1. Faculty of Engineering, Hokkei-Gakuen University, 1-1 Minami-26, Nishi 11, Chuo-ku, 064-0926, Sapporo, Hokkaido, Japan

    Toshimitsu Asakura

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Bužek, V., Drobný, G., Wiedemann, H. (1999). Quantum Tomography of Wigner Functions from Incomplete Data. In: Asakura, T. (eds) International Trends in Optics and Photonics. Springer Series in OPTICAL SCIENCES, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48886-6_5

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  • DOI: https://doi.org/10.1007/978-3-540-48886-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-14212-7

  • Online ISBN: 978-3-540-48886-6

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