Spectral representation of infimum of bounded quantum observables

TL;DR

This paper explores the spectral representation of the infimum of bounded quantum observables within a specific logical order, building on prior work that established the existence of such infima.

Contribution

It introduces a spectral representation for the infimum of subsets of bounded quantum observables under the logic order, advancing the mathematical understanding of quantum measurement theory.

Findings

Spectral representation formula for the infimum of quantum observables

Extension of existing results on the existence of infima

Enhanced mathematical framework for quantum logic

Abstract

In 2006, Gudder introduced a logic order on bounded quantum observable set $S(H)$. In 2007, Pulmannova and Vincekova proved that for each subset $\cal D$ of $S(H)$, the infimum of $\cal D$ exists with respect to this logic order. In this paper, we present the spectral representation for the infimum of $\cal D$.