The effects of different quantum feedback types on the tightness of the variance-based uncertainty

TL;DR

This paper investigates how different quantum feedback mechanisms influence the tightness of variance-based uncertainty relations, revealing relationships with system mixedness and methods to enhance uncertainty tightness.

Contribution

It demonstrates the impact of quantum feedback on the tightness of uncertainty relations and explores how feedback can be used to improve state preparation.

Findings

Tightness of SUR has a linear relationship with system mixedness.

Feedback tuning can enhance RUR tightness during evolution.

RUR tightness inversely relates to mixedness, becoming linear at steady state.

Abstract

The effect of the quantum feedback on the tightness of the variance-based uncertainty, the possibility of using quantum feedback to prepare the state with a better tightness, and the relationship between the tightness of the uncertainty and the mixedness of the system are studied. It is found that the tightness of Schrodinger-Robertson uncertainty (SUR) relation has a strict liner relationship with the mixedness of the system. As for the Robertson uncertainty relation (RUR), we find that the tightness can be enhanced by tuning the feedback at the beginning of the evolution. In addition, we deduce that the tightness of RUR has an inverse relationship with the mixedness and the relationship turns into a strict linear one when the system reach the steady state.