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Table of contents (5 chapters)
Keywords
- complex interpolation theory
- Golden-Thompson inequality
- Lieb's concavity theorem
- quantum entropy
- strong subadditivity of quantum entropy
- Lieb's triple matrix inequality
- non-commuting matrix
- quantum thermodynamics
- quantum error correction
- topological entanglement entropy
- multivariate trace inequalities
- Schatten norms
- Quantum channels
- Renyi relative entropy
- Spectral pinching method
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Approximate Quantum Markov Chains
Authors: David Sutter
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-3-319-78732-9
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Author(s) 2018
Softcover ISBN: 978-3-319-78731-2Published: 03 May 2018
eBook ISBN: 978-3-319-78732-9Published: 20 April 2018
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: VIII, 118
Number of Illustrations: 1 illustrations in colour
Topics: Quantum Physics, Mathematical Physics, Condensed Matter Physics, Statistical Physics and Dynamical Systems, Quantum Information Technology, Spintronics