Relative entropic uncertainty relation

TL;DR

This paper introduces a new form of quantum uncertainty relation based on relative entropy, applicable to both discrete and continuous observables, with a nontrivial upper bound demonstrated through examples.

Contribution

It presents a novel entropic uncertainty relation using relative entropy that applies broadly to different types of quantum observables.

Findings

Sum of relative entropies bounded from above in a nontrivial way

Applicable to observables with discrete or continuous spectra

Illustrated with specific examples

Abstract

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra. We find that a sum of relative entropies is bounded from above in a nontrivial way, which we illustrate with some examples.