Approximate Quantum Markov Chains

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book Approximate Quantum Markov Chains by David Sutter, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: David Sutter ISBN: 9783319787329
Publisher: Springer International Publishing Publication: April 20, 2018
Imprint: Springer Language: English
Author: David Sutter
ISBN: 9783319787329
Publisher: Springer International Publishing
Publication: April 20, 2018
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Progressive Business Models by David Sutter
Cover of the book Complex and Adaptive Dynamical Systems by David Sutter
Cover of the book US Environmental Policy in Action by David Sutter
Cover of the book Information and Software Technologies by David Sutter
Cover of the book Financial Environment and Business Development by David Sutter
Cover of the book Reviews of Environmental Contamination and Toxicology volume by David Sutter
Cover of the book The Future of the Postal Sector in a Digital World by David Sutter
Cover of the book Histopathology Specimens by David Sutter
Cover of the book Network Embeddedness by David Sutter
Cover of the book Experimental IR Meets Multilinguality, Multimodality, and Interaction by David Sutter
Cover of the book Concepts and Instruments for a Rational Bioenergy Policy by David Sutter
Cover of the book Computational Plasticity for Finite Elements by David Sutter
Cover of the book Natural Hazard Zonation of Bihar (India) Using Geoinformatics by David Sutter
Cover of the book Research-Based Learning: Case Studies from Maastricht University by David Sutter
Cover of the book Big Data Support of Urban Planning and Management by David Sutter
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy