States and synaptic algebras
Mathematical Physics
2017-04-05 v1 math.MP
Operator Algebras
Abstract
Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a generalization of the partially ordered Jordan algebra of all bounded self-adjoint operators on a Hilbert space. The paper culminates with a characterization of extremal states on a commutative generalized Hermitian algebra, a special kind of synaptic algebra.
Cite
@article{arxiv.1606.08229,
title = {States and synaptic algebras},
author = {David J. Foulis and Anna Jencova and Sylvia Pulmannova},
journal= {arXiv preprint arXiv:1606.08229},
year = {2017}
}