Quantum Description of Angles in the Plane

Roberto Beneduci, Emmanuel Frion, Jean-Pierre Gazeau

Published 2021-11-22, updated 2022-03-28Version 2

The real plane with its set of orientations or angles in $[0,\pi)$ is the simplest non trivial example of a (projective) Hilbert space and provides nice illustrations of quantum formalism. We present some of them, namely covariant integral quantization, linear polarisation of light as a quantum measurement, interpretation of entanglement leading to the violation of Bell inequalities, and spin one-half coherent states viewed as two entangled angles.