Entropic uncertainty relations and their applications

  title={Entropic uncertainty relations and their applications},
  author={Patrick J. Coles and Mario Berta and Marco Tomamichel and Stephanie Wehner},
  journal={Reviews of Modern Physics},
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… 

Entropic uncertainty relations from quantum designs

This work shows how to derive entropic uncertainty relations for sets of measurements whose effects form quantum designs and uses the derived uncertainty relations to investigate the incompatibility of sets of binary observables.

Multiple uncertainty relation for accelerated quantum information

The uncertainty principle, first introduced by Heisenberg in inertial frames, clearly distinguishes quantum theories from classical mechanics. In noninertial frames, its information-theoretic

Entropic uncertainty relations in a class of generalized probabilistic theories

Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about

A Framework for Uncertainty Relations

This work indicates that it seems unreasonable to assume a priori that incompatible observables have equal contribution to the variance-based sum form uncertainty relations, and investigates the uncertainty relations based on the sum of variances and derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations.

Entropic uncertainty and measurement reversibility

The entropic uncertainty relation with quantum side information (EUR-QSI) from (Berta et al 2010 Nat. Phys. 6 659) is a unifying principle relating two distinctive features of quantum mechanics:

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

The history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems.

Continuous-variable entropic uncertainty relations

  • A. HertzN. Cerf
  • Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2019
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of

Near-Optimal Variance-Based Uncertainty Relations

This work investigates the fundamental limitations of variance-based uncertainty relations, and introduces several ‘near optimal’ bounds for incompatible observables, and detailed how to formulate lower bounds for product-form variance- based uncertainty relations by employing entropic uncertainty relations.

Generalized multipartite entropic uncertainty relations: theory and experiment

Entropic uncertainty relation (EUR) plays a vital role in quantum information theories by demonstrating the intrinsic uncertainty of nature from the information-theoretic perspective. A tighter lower

Experimental investigation of entropic uncertainty relations and coherence uncertainty relations

The uncertainty relation usually is one of the most important features in quantum mechanics and is the backbone of quantum theory, which distinguishes it from the rule in its classical counterpart.



Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations

This thesis provides an information theoretic analysis by discussing entropic uncertainty relations with quantum side information and develops various kinds of quantum channel simulation results by using classical and quantum randomness extractors that also work with respect to quantum side Information.

Uncertainty, joint uncertainty, and the quantum uncertainty principle

This paper uses operational information-theoretic principles to identify the common essence of all measure-independent notions of uncertainty and joint uncertainty, finding that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a small class of operational interpretations.

Security of quantum key distribution

  • R. Renner
  • Computer Science
    Ausgezeichnete Informatikdissertationen
  • 2005
This work proposes an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold, and introduces new uncertainty measures, called smooth min- and max-entropy, which are generalizations of information-theoretical notions.

A framework for non-asymptotic quantum information theory

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography, and introduces the purified distance, a novel metric for unnormalized quantum states, and explores various properties of these entropies, including data-processing inequalities, chain rules and their classical limits.

Quantum Information Processing with Finite Resources - Mathematical Foundations

This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices, and introduces the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states.

Quantum entropy and its use

Entropy is a central quantity in information theory, probability and physics. This spring school will focus on fundamental concepts and basic operational interpretations of entropy with a particular

The principle behind the Uncertainty Principle

Department of Mathematics and Statistics and Institute for Quantum Science and Technology,University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4(Dated: May 12, 2015)Whilst

Asymptotic entropic uncertainty relations

This work analyzes entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases and develops estimates on the maximum operator norm of a submatrix of a fixed size of a random unitary matrix distributed according to the Haar measure, which are of an independent interest.

Entropic uncertainty relations for incomplete sets of mutually unbiased observables

Relations in the intermediate regime of large, but far from complete, sets of unbiased observables are explored, including relationships between `mutually unbiased' observables, which are maximally incompatible.

Quantum cryptography beyond quantum key distribution

This review article, aimed primarily at cryptographers unfamiliar with the quantum world, survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.