Quantum Description of Angles in the Plane

Abstract

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.

8 pages. Matches the published version in the AAMP Special Issue of the diamond Open-Access journal Acta Polytechnica

References in corpus (1)

• Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light