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The Resource Approximate Quantum Markov Chains, by David Sutter, (electronic resource)
Approximate Quantum Markov Chains, by David Sutter, (electronic resource)
Resource Information
The item Approximate Quantum Markov Chains, by David Sutter, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Approximate Quantum Markov Chains, by David Sutter, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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
 VIII, 118 p. 1 illus. in color.
 Contents

 Introduction
 Classical Markov chains
 Quantum Markov chains
 Outline
 Preliminaries
 Notation
 Schatten norms
 Functions on Hermitian operators
 Quantum channels
 Entropy measures
 Background and further reading
 Tools for noncommuting operators
 Pinching
 Complex interpolation theory
 Background and further reading
 Multivariate trace inequalities
 Motivation
 Multivariate ArakiLiebThirring inequality
 Multivariate GoldenThompson inequality
 Multivariate logarithmic trace inequality
 Background and further reading
 Approximate quantum Markov chains
 Quantum Markov chains
 Sufficient criterion for approximate recoverability
 Necessary criterion for approximate recoverability
 Strengthened entropy inequalities
 Background and further reading
 A A large conditional mutual information does not imply bad recovery
 B Example showing the optimality of the Lmaxterm
 C Solutions to exercises
 References
 Index
 Isbn
 9783319787329
 Label
 Approximate Quantum Markov Chains
 Title
 Approximate Quantum Markov Chains
 Statement of responsibility
 by David Sutter
 Subject

 Mathematical physics
 Mathematical physics
 Physics
 Physics
 Physics
 Quantum Information Technology, Spintronics
 Quantum Physics
 Quantum computers
 Quantum computers
 Quantum theory
 Quantum theory
 Spintronics
 Spintronics
 Statistical Physics and Dynamical Systems
 Condensed Matter Physics
 Condensed matter
 Condensed matter
 Electronic resources
 Mathematical Physics
 Mathematical Physics
 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
 http://library.link/vocab/creatorName
 Sutter, David
 Image bit depth
 0
 LC call number
 QC173.96174.52
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 SpringerBriefs in Mathematical Physics,
 Series volume
 28
 http://library.link/vocab/subjectName

 Physics
 Mathematical physics
 Quantum theory
 Condensed matter
 Quantum computers
 Spintronics
 Physics
 Quantum Physics
 Mathematical Physics
 Condensed Matter Physics
 Statistical Physics and Dynamical Systems
 Quantum Information Technology, Spintronics
 Label
 Approximate Quantum Markov Chains, by David Sutter, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Classical Markov chains  Quantum Markov chains  Outline  Preliminaries  Notation  Schatten norms  Functions on Hermitian operators  Quantum channels  Entropy measures  Background and further reading  Tools for noncommuting operators  Pinching  Complex interpolation theory  Background and further reading  Multivariate trace inequalities  Motivation  Multivariate ArakiLiebThirring inequality  Multivariate GoldenThompson inequality  Multivariate logarithmic trace inequality  Background and further reading  Approximate quantum Markov chains  Quantum Markov chains  Sufficient criterion for approximate recoverability  Necessary criterion for approximate recoverability  Strengthened entropy inequalities  Background and further reading  A A large conditional mutual information does not imply bad recovery  B Example showing the optimality of the Lmaxterm  C Solutions to exercises  References  Index
 Dimensions
 unknown
 Extent
 VIII, 118 p. 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319787329
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319787329
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319787329
 Label
 Approximate Quantum Markov Chains, by David Sutter, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Classical Markov chains  Quantum Markov chains  Outline  Preliminaries  Notation  Schatten norms  Functions on Hermitian operators  Quantum channels  Entropy measures  Background and further reading  Tools for noncommuting operators  Pinching  Complex interpolation theory  Background and further reading  Multivariate trace inequalities  Motivation  Multivariate ArakiLiebThirring inequality  Multivariate GoldenThompson inequality  Multivariate logarithmic trace inequality  Background and further reading  Approximate quantum Markov chains  Quantum Markov chains  Sufficient criterion for approximate recoverability  Necessary criterion for approximate recoverability  Strengthened entropy inequalities  Background and further reading  A A large conditional mutual information does not imply bad recovery  B Example showing the optimality of the Lmaxterm  C Solutions to exercises  References  Index
 Dimensions
 unknown
 Extent
 VIII, 118 p. 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319787329
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319787329
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319787329
Subject
 Mathematical physics
 Mathematical physics
 Physics
 Physics
 Physics
 Quantum Information Technology, Spintronics
 Quantum Physics
 Quantum computers
 Quantum computers
 Quantum theory
 Quantum theory
 Spintronics
 Spintronics
 Statistical Physics and Dynamical Systems
 Condensed Matter Physics
 Condensed matter
 Condensed matter
 Electronic resources
 Mathematical Physics
 Mathematical Physics
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