An improved bound for strong unitary uncertainty relations with refined sequence

TL;DR

This paper presents a tighter lower bound for uncertainty relations involving two and three unitary operators, improving upon previous bounds using geometric and algebraic inequalities, with illustrative examples.

Contribution

The paper introduces a refined method to derive tighter bounds for unitary uncertainty relations, extending the known results to three operators.

Findings

New lower bounds are tighter than previous results.

The method applies geometric-arithmetic and Cauchy-Schwarz inequalities.

Examples demonstrate the effectiveness of the bounds.

Abstract

We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three unitary operators. Compared to the known bound introduced in Phys.Rev.A.100,022116(2019), the unitary uncertainty relations bound with our method is tighter, to a certain extent. Meanwhile, some examples are given in the paper to illustrate our conclusions.