Improved entropic uncertainty relations and information exclusion relations

TL;DR

This paper presents improved formulations of entropic uncertainty and information exclusion relations, enhancing their applications in quantum security, entanglement estimation, and communication by providing more stringent bounds and clarifying fundamental distinctions.

Contribution

It introduces tighter entropic uncertainty and information exclusion relations, with direct implications for quantum information tasks and a fundamental distinction between observable complementarity in uncertainty and information.

Findings

Stronger bounds for entropic uncertainty relations.

Enhanced information exclusion principles for quantum correlations.

Clarification of the difference between uncertainty and information complementarity.

Abstract

The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes of incompatible measurements on one physical system, and a second reference system. We provide a more stringent formulation of both the uncertainty principle and the information exclusion principle, with direct applications for, e.g., the security analysis of quantum key distribution, entanglement estimation, and quantum communication. We also highlight a fundamental distinction between the complementarity of observables in terms of uncertainty and in terms of information.