Entropic Uncertainty Relations and their Applications

TL;DR

This paper reviews entropic uncertainty relations in quantum mechanics, highlighting their foundational significance and applications in quantum cryptography, entanglement detection, and wave-particle duality, including recent generalizations involving quantum correlations.

Contribution

It provides a comprehensive survey of entropic uncertainty relations, covering finite and infinite dimensions, and discusses recent extensions incorporating quantum correlations and diverse applications.

Findings

Entropic uncertainty relations underpin quantum cryptography security.

Extensions include quantum correlations between system and environment.

Applications span entanglement witnessing, wave-particle duality, and more.

Abstract

Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. More recently, entropic uncertainty relations have emerged as the central ingredient in the security analysis of almost all quantum cryptographic protocols, such as quantum key distribution and two-party quantum cryptography. This review surveys entropic uncertainty relations that capture Heisenberg's idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements. These ideas are then extended to incorporate quantum correlations between the observed object and its environment, allowing for a variety of recent, more general formulations of the uncertainty principle. Finally, various applications are discussed, ranging from entanglement witnessing to wave-particle duality to quantum cryptography.