Approximate Quantum Markov Chains

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 statem...

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Bibliographische Detailangaben
1. Verfasser: Sutter, David (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:1st ed. 2018.
Schriftenreihe:SpringerBriefs in Mathematical Physics, 28
Schlagworte:
Quantum physics.
Mathematical physics.
Condensed matter.
Statistical physics.
Quantum computers.
Spintronics.
ISBN:9783319787329
ISSN:2197-1757 ;
Online-Zugang: Volltext
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Inhaltsangabe:
  • 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.

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