Entropic uncertainty relation for pointer-based simultaneous measurements of conjugate observables

TL;DR

This paper introduces entropic uncertainty relations for simultaneous measurements of conjugate observables, explicitly accounting for measurement apparatus effects, and identifies squeezed states as minimal entropy states.

Contribution

It develops a family of entropic uncertainty relations that include measurement device influence, advancing understanding of measurement limits in quantum mechanics.

Findings

Squeezed states minimize measurement entropy.

Lower bounds depend explicitly on measurement apparatus.

Theoretical framework uses convolution entropy bounds.

Abstract

We present a family of entropic uncertainty relations for pointer-based simultaneous measurements of conjugate observables. The lower bounds of these relations explicitly incorporate the influence of the measurement apparatus. We achieve this by using a mathematical theorem which states that the information entropy of convoluted probability distributions is bound from below. As a consequence of these results we can straightforwardly show that appropriately squeezed states are minimal entropy states for simultaneous measurements.