States and synaptic algebras

TL;DR

This paper explores the relationships between states on synaptic algebras and their sub-structures, providing a characterization of extremal states on a specific class of these algebras, generalizing quantum structures.

Contribution

It introduces a detailed analysis of states on synaptic algebras and characterizes extremal states on commutative generalized Hermitian algebras, expanding the understanding of quantum algebraic structures.

Findings

Characterization of extremal states on commutative generalized Hermitian algebras

Analysis of the interplay among states on synaptic algebras and sub-structures

Generalization of states in quantum structures

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.