An uncertainty relation in the case of four observables

TL;DR

This paper introduces a tight uncertainty relation for four quantum observables using matrix theory, unifying previous relations for multiple observables and comparing its effectiveness with existing ones.

Contribution

It presents a novel, tight uncertainty relation for four observables, extending and unifying the framework for multiple quantum measurements.

Findings

The uncertainty constant is tight.

The method unifies uncertainty relations for two, three, and four observables.

Comparison shows advantages over existing relations.

Abstract

Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is argued that this method can deal with the several known uncertainty relations for two, three and four observables in a unified way. The result is also compared with other uncertainty relations of four observables.