Quantum Uncertainty and Entropy

TL;DR

This paper reviews various quantum uncertainty relations, highlighting their foundational and practical applications in areas like quantum metrology and cryptography, covering both variance- and entropy-based approaches.

Contribution

It provides a comprehensive overview of quantum uncertainty relations, emphasizing their nuanced differences and applications in foundational and practical quantum physics.

Findings

Detailed comparison of variance- and entropy-based uncertainty relations

Applications in quantum metrology and cryptography

Clarification of foundational concepts like complementarity

Abstract

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum metrology and cryptography. Both variance- and entropy-based uncertainties are covered here.