Unsharpness of generalized measurement and its effects in entropic uncertainty relations

TL;DR

This paper introduces a new entropic uncertainty relation that separates quantum uncertainty from measurement device imperfections, quantified by Shannon entropy, and explores its implications under various noisy measurement scenarios.

Contribution

It proposes a novel class of entropic uncertainty relations that explicitly account for measurement unsharpness, enhancing understanding of measurement-induced quantum uncertainty.

Findings

Derived a new lower bound for entropic uncertainty considering unsharpness.

Showed the relation applies to noisy sharp observables affected by white noise and amplitude damping.

Quantified measurement device uncertainty using Shannon entropy.

Abstract

Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we suggest a new class of entropic uncertainty relation that differentiates quantum uncertainty from device imperfection due to the unsharpness of measurement. In order to quantify the unsharpness, we {suggest} and analyze the quantity that characterizes the uncertainty in the measuring device, based on Shannon entropy. Using the quantity, we obtain a new lower bound of entropic uncertainty with unsharpness and it has been shown that the relation can also be obtained under the scenario that sharp observables are affected by the white noise and amplitude damping.