Uncertainty relations for metric adjusted skew information and Cauchy-Schwarz inequality

TL;DR

This paper refines uncertainty relations in quantum information using metric-adjusted skew information, employing sampling coordinates and convex functions to improve bounds for multiple observables.

Contribution

It introduces new methods to tighten uncertainty bounds based on metric-adjusted skew information for multiple quantum observables.

Findings

Refined uncertainty relations for two observables.

Enhanced bounds for sums of multiple observables.

Application of convex functions and sampling coordinates in quantum uncertainty.

Abstract

Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an in-depth investigation using the methodologies of sampling coordinates of observables and convex functions to refine the uncertainty relations in both the product form of two observables and summation form of multiple observables.