The Resource Approximate Quantum Markov Chains, by David Sutter, (electronic resource)

Approximate Quantum Markov Chains, by David Sutter, (electronic resource)

Label
Approximate Quantum Markov Chains
Title
Approximate Quantum Markov Chains
Statement of responsibility
by David Sutter
Creator
Contributor
Author
Provider
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
http://library.link/vocab/creatorName
Sutter, David
Image bit depth
0
LC call number
QC173.96-174.52
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)
Instantiates
Publication
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 non-commuting operators -- Pinching -- Complex interpolation theory -- Background and further reading -- Multivariate trace inequalities -- Motivation -- Multivariate Araki-Lieb-Thirring inequality -- Multivariate Golden-Thompson 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 Lmax-term -- 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
10.1007/978-3-319-78732-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-78732-9
Label
Approximate Quantum Markov Chains, by David Sutter, (electronic resource)
Publication
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 non-commuting operators -- Pinching -- Complex interpolation theory -- Background and further reading -- Multivariate trace inequalities -- Motivation -- Multivariate Araki-Lieb-Thirring inequality -- Multivariate Golden-Thompson 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 Lmax-term -- 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
10.1007/978-3-319-78732-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-78732-9

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