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The Resource Approximate quantum Markov chains, David Sutter, (electronic book)

Approximate quantum Markov chains, David Sutter, (electronic book)

Label
Approximate quantum Markov chains
Title
Approximate quantum Markov chains
Statement of responsibility
David Sutter
Creator
Author
Subject
Language
eng
Summary
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple matrix inequality can be extended to more than three matrices. Finally, we carefully discuss the properties of approximate quantum Markov chains and their implications. The book is aimed to graduate students who want to learn about approximate quantum Markov chains as well as more experienced scientists who want to enter this field. Mathematical majority is necessary, but no prior knowledge of quantum mechanics is required
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Sutter, David
Dewey number
519.2/33
Index
index present
LC call number
QA274.7
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Springer briefs in mathematical physics
Series volume
volume 28
http://library.link/vocab/subjectName
  • Markov processes
  • Physics
  • Quantum Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Statistical Physics and Dynamical Systems
  • Quantum Information Technology, Spintronics
Label
Approximate quantum Markov chains, David Sutter, (electronic book)
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Acknowledgements; Contents; 1 Introduction; 1.1 Classical Markov Chains; 1.1.1 Robustness of Classical Markov Chains; 1.2 Quantum Markov Chains; 1.2.1 Robustness of Quantum Markov Chains; 1.3 Outline; References; 2 Preliminaries; 2.1 Notation; 2.2 Schatten Norms; 2.3 Functions on Hermitian Operators; 2.4 Quantum Channels; 2.5 Entropy Measures; 2.5.1 Fidelity; 2.5.2 Relative Entropy; 2.5.3 Measured Relative Entropy; 2.5.4 Rényi Relative Entropy; 2.6 Background and Further Reading; References; 3 Tools for Non-commuting Operators; 3.1 Pinching; 3.1.1 Spectral Pinching
  • 3.1.2 Smooth Spectral Pinching3.1.3 Asymptotic Spectral Pinching; 3.2 Complex Interpolation Theory; 3.3 Background and Further Reading; References; 4 Multivariate Trace Inequalities; 4.1 Motivation; 4.2 Multivariate Araki-Lieb-Thirring Inequality; 4.3 Multivariate Golden-Thompson Inequality; 4.4 Multivariate Logarithmic Trace Inequality; 4.5 Background and Further Reading; References; 5 Approximate Quantum Markov Chains; 5.1 Quantum Markov Chains; 5.2 Sufficient Criterion for Approximate Recoverability; 5.2.1 Approximate Markov Chains are not Necessarily Close to Markov Chains
Extent
1 online resource.
Form of item
online
Isbn
9783319787329
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-78732-9
System control number
  • on1032070700
  • (OCoLC)1032070700
Label
Approximate quantum Markov chains, David Sutter, (electronic book)
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Acknowledgements; Contents; 1 Introduction; 1.1 Classical Markov Chains; 1.1.1 Robustness of Classical Markov Chains; 1.2 Quantum Markov Chains; 1.2.1 Robustness of Quantum Markov Chains; 1.3 Outline; References; 2 Preliminaries; 2.1 Notation; 2.2 Schatten Norms; 2.3 Functions on Hermitian Operators; 2.4 Quantum Channels; 2.5 Entropy Measures; 2.5.1 Fidelity; 2.5.2 Relative Entropy; 2.5.3 Measured Relative Entropy; 2.5.4 Rényi Relative Entropy; 2.6 Background and Further Reading; References; 3 Tools for Non-commuting Operators; 3.1 Pinching; 3.1.1 Spectral Pinching
  • 3.1.2 Smooth Spectral Pinching3.1.3 Asymptotic Spectral Pinching; 3.2 Complex Interpolation Theory; 3.3 Background and Further Reading; References; 4 Multivariate Trace Inequalities; 4.1 Motivation; 4.2 Multivariate Araki-Lieb-Thirring Inequality; 4.3 Multivariate Golden-Thompson Inequality; 4.4 Multivariate Logarithmic Trace Inequality; 4.5 Background and Further Reading; References; 5 Approximate Quantum Markov Chains; 5.1 Quantum Markov Chains; 5.2 Sufficient Criterion for Approximate Recoverability; 5.2.1 Approximate Markov Chains are not Necessarily Close to Markov Chains
Extent
1 online resource.
Form of item
online
Isbn
9783319787329
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-78732-9
System control number
  • on1032070700
  • (OCoLC)1032070700

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