POVM Quantization
Quantum Physics
2019-11-06 v1 Mathematical Physics
math.MP
Abstract
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by points of the measure space. We specially focus on various probabilistic aspects of these constructions. Simple or more elaborate examples illustrate the procedure: circle, 2-sphere, plane, half-plane. Links with POVM quantum measurement and quantum statistical inference are sketched.
Cite
@article{arxiv.1408.6090,
title = {POVM Quantization},
author = {Jean Pierre Gazeau and Barbara Heller},
journal= {arXiv preprint arXiv:1408.6090},
year = {2019}
}