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Hermite Polynomial Representation of Qubit States in Quantum Suprematism Picture

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Classical and Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 229))

Abstract

We consider the Hermite polynomial representation (H-representation) of spin states for qubits and qudits in quantum suprematism picture, where the state geometry is illustrated by Triadas of Malevich’s squares. We obtain an explicit connection of the density matrices of qubit states with the wave functions of two-dimensional harmonic oscillators and the probabilities identified with the states. We establish the connection of optical tomographic-probability distributions describing the oscillator states with qudit state tomograms.

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    Margarita A. Man’ko & Vladimir I. Man’ko

Authors
  1. Margarita A. Man’ko
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  2. Vladimir I. Man’ko
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Corresponding author

Correspondence to Vladimir I. Man’ko .

Editor information

Editors and Affiliations

  1. Università degli Studi di Napoli Federico II, Naples, Italy

    G. Marmo

  2. Institute of Mathematical Sciences (ICMAT), Madrid, Spain

    David Martín de Diego

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Miguel Muñoz Lecanda

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Man’ko, M.A., Man’ko, V.I. (2019). Hermite Polynomial Representation of Qubit States in Quantum Suprematism Picture. In: Marmo, G., Martín de Diego, D., Muñoz Lecanda, M. (eds) Classical and Quantum Physics. Springer Proceedings in Physics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-24748-5_16

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