Uncertainty, joint uncertainty, and the quantum uncertainty principle

TL;DR

This paper introduces a measure-independent framework for quantum uncertainty, revealing new joint uncertainty measures and deriving novel uncertainty relations using information-theoretic principles.

Contribution

It develops a unified, operational approach to quantify quantum uncertainty, expanding beyond traditional entropic measures and providing new insights into uncertainty relations.

Findings

Most existing entropic uncertainty relations use limited measures of joint uncertainty.

The new formalism uncovers previously unexplored joint uncertainty measures.

An uncertainty relation based on a novel measure is derived.

Abstract

Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a small class of operational interpretations. Our notion relaxes this restriction, revealing previously unexplored joint uncertainty measures. To illustrate the utility of our formalism, we derive an uncertainty relation based on one such new measure. We also use our formalism to gain insight into the conditions under which measure-independent uncertainty relations can be found.