A geometric way to find the measures of uncertainty from statistical divergences for discrete and finite probability distributions

TL;DR

This paper introduces a geometric framework to derive uncertainty measures from statistical divergences for discrete distributions and quantum states, revealing new measures and their properties.

Contribution

It presents a novel geometric approach to define and analyze uncertainty measures from divergences, including new measures and applications to quantum state preparation.

Findings

New uncertainty measures derived from statistical divergences.

Properties of these measures are analyzed.

Application to quantum state uncertainty measurement.

Abstract

Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their properties. Further, we apply a similar technique to measure the uncertainty in the preparation of a quantum state.