Approximate Quantum Markov Chains [E-Book] / by David Sutter.
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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Full text |
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Personal Name(s): | Sutter, David, author |
Edition: |
1st ed. 2018. |
Imprint: |
Cham :
Springer,
2018
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Physical Description: |
VIII, 118 pages 1 illustrations in color (online resource) |
Note: |
englisch |
ISBN: |
9783319787329 |
DOI: |
10.1007/978-3-319-78732-9 |
Series Title: |
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SpringerBriefs in Mathematical Physics ;
28 |
Subject (LOC): |
- 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.