Stronger Error Disturbance Relations for Incompatible Quantum Measurements

TL;DR

This paper introduces a new error-disturbance relation in quantum measurements that improves upon existing inequalities by providing tighter bounds for certain states and measurement classes.

Contribution

It formulates a novel error-disturbance relation independent of observable variances and proves a modified, tighter form of Ozawa's relation.

Findings

New error-disturbance relation outperforms Branciard and Ozawa inequalities for some states.

Modified Ozawa relation provides tighter bounds for specific states.

Improves understanding of measurement disturbance in quantum mechanics.

Abstract

We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa inequality for some initial states and for particular class of joint measurements under consideration. We also prove a modified form of Ozawa's error-disturbance relation. The later relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states.