On the representations of Bell's operators in Quantum Mechanics
Quantum Physics
2023-06-14 v3
Abstract
We point out that, when the dimension of the Hilbert space is greater than two, Bell's operators entering the Bell-CHSH inequality exhibit unitarily inequivalent representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson's bound. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.
Cite
@article{arxiv.2304.05696,
title = {On the representations of Bell's operators in Quantum Mechanics},
author = {Silvio Paolo Sorella},
journal= {arXiv preprint arXiv:2304.05696},
year = {2023}
}
Comments
final version, 13 pages, to appear in Foundations of Physics