# Strong unitary uncertainty relations

## TL;DR

This paper introduces a new set of refined uncertainty relations for unitary operators that improve upon existing bounds by employing a sequence of inequalities, offering tighter constraints in quantum mechanics.

## Contribution

The paper presents a novel framework for unitary uncertainty relations using geometric-arithmetic mean inequalities, surpassing previous bounds based on Cauchy-Schwarz inequality.

## Key findings

- New uncertainty bounds outperform previous results in some cases
- Explicit examples demonstrate the effectiveness of the new inequalities
- The framework provides a more fine-grained approach to uncertainty relations

## Abstract

In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in [Phys. Rev. Lett. 120, 230402 (2018)] to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims.