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 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 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 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
- 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 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
- 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 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
- 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 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
- 9783319787312
- 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)
- 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
- 9783319787312
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Approximate-quantum-Markov-chains-David-Sutter/IuIHs4biOPg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Approximate-quantum-Markov-chains-David-Sutter/IuIHs4biOPg/">Approximate quantum Markov chains, David Sutter, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
