EAN: 9783319787312

APPROXIMATE QUANTUM MARKOV CHAINS - DAVID SUTTE...

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.

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