Quantum Axiomatics: Topological and Classical Properties of State Property Systems

TL;DR

This paper explores a topological approach to defining classical states in quantum systems, offering an alternative to orthocomplementation-based methods by analyzing the epsilon-model on the Poincare sphere.

Contribution

It introduces a topological notion of classicality for states in quantum systems, providing an operational alternative to traditional orthocomplementation-based definitions.

Findings

Topological classicality can be operationally defined without orthocomplementation.

The epsilon-model on the Poincare sphere illustrates the topological classicality concept.

Comparison shows topological classicality aligns with known classicality notions.

Abstract

The definition of 'classical state', and how it was used in earlier work to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property lattice of a physical system. In this paper we argue on the basis of the epsilon-model on the Poincare sphere that a notion of 'topologicity' for states can be seen as an alternative (operationally foundable) classicality notion in the absence of an orthocomplementation, and compare it to the known and operationally founded concept of classicality.