R\'enyi entropy uncertainty relation for successive projective measurements

TL;DR

This paper derives a Rényi entropy-based uncertainty relation for successive quantum measurements, providing a tighter lower bound than previous formulations, applicable to various entropy measures including Shannon entropy.

Contribution

It introduces a new uncertainty relation for successive projective measurements using Rényi entropy with an improved lower bound.

Findings

The relation covers a broad family of entropy measures including Shannon entropy.

The new bound is shown to be tighter than existing uncertainty relations.

Application to two-spin observables demonstrates the relation's effectiveness.

Abstract

We investigate the uncertainty principle for two successive projective measurements in terms of R\'enyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty relations with a lower optimal bound. We compare our relation with other formulations of the uncertainty principle in a two-spin observables measured on a pure quantum state of qubit. It is shown that the low bound of our uncertainty relation has better tightness.