The Continuity of Sequential Product of Sequential Quantum Effect Algebras

TL;DR

This paper investigates the continuity properties of the sequential product in quantum effect algebras across various topologies to better understand quantum measurement processes.

Contribution

It extends the study of the sequential product by analyzing its continuity under multiple topologies beyond the strong operator topology.

Findings

Sequential product continuity varies with different topologies.

Continuity results depend on the specific topology considered.

Provides a comprehensive analysis of continuity in quantum effect algebras.

Abstract

In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In this paper, we study the continuity problems of the sequential product with respect to the other important topologies, as norm topology, weak operator topology, order topology, interval topology, etc.