Entropic uncertainty bound for open pointer-based simultaneous measurements of conjugate observables

TL;DR

This paper derives an entropic uncertainty bound for open pointer-based measurements of conjugate observables, providing insights into how environmental noise influences measurement accuracy.

Contribution

It introduces a novel entropic uncertainty bound for open pointer-based measurements and offers an intuitive interpretation of environmental effects on measurement noise.

Findings

Derived a lower bound for entropy in open pointer measurements

Provided a formal solution linking measurement dynamics to entropy bounds

Interpreted environmental noise impact on measurement outcomes

Abstract

We discuss the information entropy for a general open pointer-based simultaneous measurement and show how it is bound from below. This entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained from the formal solution of the measurement dynamics. Furthermore, the structural properties of the entropy allow us to give an intuitive interpretation of the noisy influence of the pointers and the environmental heat bath on the measurement results.