On supremum of bounded quantum observable

TL;DR

This paper introduces a new necessary and sufficient condition for the existence of the supremum of bounded quantum observables under the logic order, along with a simplified representation that has clear physical interpretations.

Contribution

It provides a novel criterion and a simplified representation for the supremum of bounded quantum observables, enhancing understanding in quantum logic.

Findings

New necessary and sufficient condition for supremum existence

Simplified representation of the supremum with physical meaning

Improved understanding of quantum observable order structure

Abstract

In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our results have nice physical meanings.