Detecting mixedness of qutrit systems using the uncertainty relation

TL;DR

This paper demonstrates that the Robertson-Schrodinger uncertainty relation can be employed to detect the mixedness of qutrit systems by measuring expectation values of specific observables, linking uncertainty to the system's purity.

Contribution

It introduces a method to identify mixedness in qutrit systems using the generalized uncertainty relation and measurable observables, connecting uncertainty with linear entropy.

Findings

Uncertainty relation equality for pure states

Strict inequality for mixed states

Uncertainty magnitude proportional to linear entropy

Abstract

We show that the uncertainty relation as expressed in the Robertson-Schrodinger generalized form can be used to detect the mixedness of three-level quantum systems in terms of measureable expectation values of suitably chosen observables when prior knowledge about the basis of the given state is known. In particular, we demonstrate the existence of observables for which the generalized uncertainty relation is satisfied as an equality for pure states and a strict inequality for mixed states corresponding to single as well as bipartite sytems of qutrits. Examples of such observables are found for which the magnitude of uncertainty is proportional to the linear entropy of the system, thereby providing a method for measuring mixedness.