SU(2) symmetry of qubit states and Heisenberg-Weyl symmetry of systems with continuous variables in the probability representation of quantum mechanics

Peter Adam, Vladimir A. Andreev, Margarita A. Man'ko, Vladimir I. Man'ko, Matyas Mechler

Research output: Contribution to journalArticle

Abstract

In view of the probabilistic quantizer-dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the SU(2) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ±1/2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrodinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer-dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg-Weyl symmetry properties.

Original languageEnglish
Article number1099
JournalSymmetry
Volume12
Issue number7
DOIs
Publication statusPublished - Jul 2020

Keywords

  • Probability representation
  • Quantizer-dequantizer
  • Quantum tomography
  • Qubit

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

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