The Resource Approximate quantum Markov chains, David Sutter, (electronic book)
Approximate quantum Markov chains, David Sutter, (electronic book)
Resource Information
The item Approximate quantum Markov chains, David Sutter, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Approximate quantum Markov chains, David Sutter, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.
This item is available to borrow from 1 library branch.
 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 dataprocessing 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 noncommuting 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 GoldenThompson 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
 Language
 eng
 Extent
 1 online resource.
 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 Noncommuting 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 ArakiLiebThirring Inequality; 4.3 Multivariate GoldenThompson 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
 Isbn
 9783319787312
 Label
 Approximate quantum Markov chains
 Title
 Approximate quantum Markov chains
 Statement of responsibility
 David Sutter
 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 dataprocessing 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 noncommuting 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 GoldenThompson 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
 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)
 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 Noncommuting 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 ArakiLiebThirring Inequality; 4.3 Multivariate GoldenThompson 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
 9783319787312
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319787329
 System control number

 on1032070700
 (OCoLC)1032070700
 Label
 Approximate quantum Markov chains, David Sutter, (electronic book)
 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 Noncommuting 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 ArakiLiebThirring Inequality; 4.3 Multivariate GoldenThompson 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
 9783319787312
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319787329
 System control number

 on1032070700
 (OCoLC)1032070700
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