The role of relative entropy in quantum information theory

@article{Vedral2002TheRO,
  title={The role of relative entropy in quantum information theory},
  author={Vlatko Vedral},
  journal={Reviews of Modern Physics},
  year={2002},
  volume={74},
  pages={197-234}
}
  • V. Vedral
  • Published 19 February 2001
  • Physics
  • Reviews of Modern Physics
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates… 
Measures and applications of quantum correlations
TLDR
This work gives an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states, and focuses on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives.
Foundations of quantum theory and quantum information applications
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and
CORRELATIONS IN QUANTUM PHYSICS
We provide a historical perspective of how the notion of correlations has evolved within quantum physics. We begin by reviewing Shannon's information theory and its first application in quantum
Some Theory and Applications of Probability in Quantum Mechanics
TLDR
It is proved that quantum states are more difficult to estimate than their classical counterparts by finding optimal estimation strategies, requiring the solution to a difficult optimization problem, are difficult to implement in practise.
Bounding generalized relative entropies: Nonasymptotic quantum speed limits.
TLDR
By considering a general unitary channel, this work establishes a bound on the generalized relative entropies (Rényi and Tsallis) between the output and the input of the channel, and derives a family of quantum speed limits based on relative entropy.
The classical-quantum boundary for correlations: Discord and related measures
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical
Preamble Probability Density Operators Spectral Theorem Postscript Introduction to quantum information processing Measurements and quantum probability
TLDR
The topic of these lectures lies in the new and rapidly growing field of quantum computing, which explores connections between physics and computing in general and deepened understanding of the relationship between physics, information and computation in general.
Resource theories of quantum coherence: foundations and applications
TLDR
This thesis concentrates on understanding quantum coherence in the mathematical framework of resource theories, viewing it both as a resource to be harnessed and as a way to quantitatively characterise quantum states in contrast to classical states.
Relative entropy between quantum ensembles
TLDR
This paper proposes a notion of relative entropy between quantum ensembles, which is a natural generalization of the relative entropyBetween quantum states, and demonstrates that a set consisting of two pure states is the most quantum when the states are 45° apart.
HIERARCHY OF CORRELATIONS VIA LÜDERS MEASUREMENTS
The classification and quantification of correlations (classical and quantum) in composite quantum systems are of fundamental significance for quantum information processing. While the paradigm of
...
...

References

SHOWING 1-10 OF 137 REFERENCES
Distinguishability and Accessible Information in Quantum Theory
TLDR
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states, and gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth
Separability and distillability in composite quantum systems-a primer
TLDR
This article presents a primer on the current state of knowledge concerning two problems of quantum information theory, and discusses the relation of these problems to one of the most challenging questions of linear algebra: the classification and characterization of positive operator maps.
Quantum Theory: Concepts and Methods
Preface. Part I: Gathering the Tools. 1. Introduction to Quantum Physics. 2. Quantum Tests. 3. Complex Vector Space. 4. Continuous Variables. Part II: Cryptodeterminism and Quantum Inseparability. 5.
PRINCIPLES OF STATISTICAL MECHANICS
These lectures comprise an introductory course in statistical mechanics. The Gibbs formulation of the canonical ensemble is introduced and illustrated by application to simple models of magnets and
Relative entropy in quantum information theory
TLDR
The properties of the quantum relative entropy function are reviewed and its application to problems of classical and quantum information transfer and to quantum data compression is discussed.
A fast quantum mechanical algorithm for database search
TLDR
In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .
Quantum lower bounds by polynomials
TLDR
This work examines the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}/sup N/ in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.
Probabilistic and Statistical Aspects of Quantum Theory
Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV.
Quantum lower bounds by quantum arguments
TLDR
Two new Ω(√N) lower bounds on computing AND of ORs and inverting a permutation and more uniform proofs for several known lower bounds which have been previously proven via a variety of different techniques are proved.
...
...