XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Hans Kastrup## Wigner functions for the pair angle and orbital angular momentum with applications to quantum informationCharacterizing the angle phi geometrically by the pair $[\cos(\phi), \sin(\phi)]$, the Poisson brackets of that pair with the the orbital angular momentum (OAM) $p$ generate the Lie algebra of the Euclidean group $E(2)$ of the plane. The unitary representations of $E(2)$ then serve to construct Wigner functions on the 2-dimensional phase space $P_{\phi,p}$, essentially by group averaging [PRA 94(2016)062113, 95(2017)052111]. Applications to quantum information concepts like qubits and 2-qubits are discussed, e.g. in view of quantum information experiments with OAM of light beams [arXiv: 1710.06359]. |

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University of Bialystok |

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