Approximate Quantum Markov Chains

• Main Author: Sutter, David (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: SpringerBriefs in Mathematical Physics, 28
• Subjects: Quantum physics.; Mathematical physics.; Condensed matter.; Statistical physics.; Quantum computers.; Spintronics.; Quantum Physics.; Mathematical Physics.; Condensed Matter Physics.; Statistical Physics and Dynamical Systems.; Quantum Information Technology, Spintronics.

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...

Table of 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.