Symplectic geometry of quantum noise
Symplectic Geometry
2016-05-11 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
We discuss a quantum counterpart, in the sense of the Berezin-Toeplitz quantization, of certain constraints on Poisson brackets coming from "hard" symplectic geometry. It turns out that they can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics. Our findings include various geometric mechanisms of quantum noise production and a noise-localization uncertainty relation. The methods involve Floer theory and Poisson bracket invariants originated in function theory on symplectic manifolds.
Keywords
Cite
@article{arxiv.1206.3707,
title = {Symplectic geometry of quantum noise},
author = {Leonid Polterovich},
journal= {arXiv preprint arXiv:1206.3707},
year = {2016}
}
Comments
Revised version, 57 pages, 3 figures. Incorporates arXiv:1203.2348