Improved unitary uncertainty relations

TL;DR

This paper develops improved variance-based uncertainty relations for multiple unitary operators by strengthening mathematical inequalities, leading to tighter bounds than previous results.

Contribution

It introduces a novel method to derive stronger uncertainty relations for unitary operators using brackets and convex functions, surpassing existing bounds.

Findings

Outperforms previous unitary uncertainty bounds

Provides tighter variance-based uncertainty relations

Applicable to multiple unitary operators

Abstract

We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz inequality using a method of brackets and convex functions. The unitary uncertainty relations outperform several strong unitary uncertainty relations, notably better than some recent best lower bounds such as [Phys. Rev. Lett. 120, 230402 (2018)] and [Phys. Rev. A. 100, 022116 (2019)].