عنوان

Approximate quantum Markov chains /

شابک

3319787322

شابک

9783319787329

شابک اشتباه

3319787314

شابک اشتباه

9783319787312

عنوان اصلي

Approximate quantum Markov chains /

نام عام مواد

[Book]

نام نخستين پديدآور

David Sutter.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

[2018]

تاریخ نشرو بخش و غیره

©2018

نام خاص و کميت اثر

1 online resource

عنوان فروست

Springer briefs in mathematical physics ;

مشخصه جلد

volume 28

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Intro; Acknowledgements; Contents; 1 Introduction; 1.1 Classical Markov Chains; 1.1.1 Robustness of Classical Markov Chains; 1.2 Quantum Markov Chains; 1.2.1 Robustness of Quantum Markov Chains; 1.3 Outline; References; 2 Preliminaries; 2.1 Notation; 2.2 Schatten Norms; 2.3 Functions on Hermitian Operators; 2.4 Quantum Channels; 2.5 Entropy Measures; 2.5.1 Fidelity; 2.5.2 Relative Entropy; 2.5.3 Measured Relative Entropy; 2.5.4 Rényi Relative Entropy; 2.6 Background and Further Reading; References; 3 Tools for Non-commuting Operators; 3.1 Pinching; 3.1.1 Spectral Pinching.

متن يادداشت

3.1.2 Smooth Spectral Pinching3.1.3 Asymptotic Spectral Pinching; 3.2 Complex Interpolation Theory; 3.3 Background and Further Reading; References; 4 Multivariate Trace Inequalities; 4.1 Motivation; 4.2 Multivariate Araki-Lieb-Thirring Inequality; 4.3 Multivariate Golden-Thompson Inequality; 4.4 Multivariate Logarithmic Trace Inequality; 4.5 Background and Further Reading; References; 5 Approximate Quantum Markov Chains; 5.1 Quantum Markov Chains; 5.2 Sufficient Criterion for Approximate Recoverability; 5.2.1 Approximate Markov Chains are not Necessarily Close to Markov Chains.

بدون عنوان

0

بدون عنوان

8

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783319787329

عنوان

Approximate quantum Markov chains.

شماره استاندارد بين المللي کتاب و موسيقي

9783319787312

موضوع مستند نشده

Markov processes.

موضوع مستند نشده

Condensed Matter Physics.

موضوع مستند نشده

Mathematical Physics.

موضوع مستند نشده

Physics.

موضوع مستند نشده

Quantum Information Technology, Spintronics.

موضوع مستند نشده

Quantum Physics.

موضوع مستند نشده

Statistical Physics and Dynamical Systems.

موضوع مستند نشده

Markov processes.

موضوع مستند نشده

Materials-- States of matter.

موضوع مستند نشده

Mathematical physics.

موضوع مستند نشده

MATHEMATICS-- Applied.

موضوع مستند نشده

MATHEMATICS-- Probability & Statistics-- General.

موضوع مستند نشده

Quantum physics (quantum mechanics & quantum field theory)

موضوع مستند نشده

Statistical physics.

موضوع مستند نشده

MAT-- 003000

موضوع مستند نشده

MAT-- 029000

موضوع مستند نشده

PHQ

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Sutter, David

تاريخ عمليات

20200823113711.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y