Entropic uncertainty relations—a survey

2009/07/21 by Stephanie Wehner, Andreas Winter · 18 citations
Computer Science · Physics and Astronomy · #Entropic uncertainty #Entropy (arrow of time) #Foundation (evidence) #Measurement uncertainty #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum measurement #quant-ph

paper · pdf · doi:10.1088/1367-2630/12/2/025009

published as New Journal of Physics - Special Issue on Quantum Information and Many-Body Theory, 12, 025009 (2010) · 12 pages, revtex

arxiv created 2009/07/21 · openalex publication_date 2010/02/26 · arxiv updated 2011/05/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, little is known about entropic uncertainty relations with more than two measurement settings. In the present survey, we review known results and open questions.

Citations

• Randomizing Quantum States: Constructions and Applications
• A Mathematical Theory of Communication
• Almost-periodic time observables for bound quantum systems
• The Uncertainty Principle
• Cryptography from Noisy Storage
• Entanglement detection in the stabilizer formalism
• �ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
• Inequalities in Fourier Analysis
• State Discrimination With Post-Measurement Information
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II

Cited by

• Beyond Robertson-Schrödinger: A General Uncertainty Relation Unveiling Hidden Noncommutative Trade-offs
• The uncertainty geometry of finite-dimensional position and momentum
• Entropic uncertainty relations and their applications
• Quantum-memory-assisted entropic uncertainty relation under noise
• The role of interparticle interaction and environmental coupling in a two-particle open quantum system
• Entanglement detection with scrambled data
• Correlation Complementarity Yields Bell Monogamy Relations
• Towards Quantum One-Time Memories from Stateless Hardware
• Uncertainty Relations from Simple Entropic Properties
• On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”
• Separability and Entanglement of a Spin-1 Particle
• Deformed Entropic and Information Inequalities forX-States of Two-Qubit and Single Qudit States
• Realization of mutually unbiased bases for a qubit with only one wave plate: theory and experiment
• A monogamy-of-entanglement game with applications to device-independent quantum cryptography
• Complementary properties of multiphoton quantum states in linear optics networks
• Flavor-mass majorization uncertainty relations and their links to the mixing matrix
• Rényi entropy of the totally asymmetric exclusion process
• Entropic trade-off relations for quantum operations

Related

• Entropic uncertainty relations and their applications
• Entropic Uncertainty for Biased Measurements
• The Trivial Bound of Entropic Uncertainty Relations
• Uncertainty Relation for Smooth Entropies
• Uncertainty relations in terms of generalized entropies derived from information diagrams