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Resources of the Quantum World

Gilad Gour

TL;DR

Providing the latest developments in the field as well as established knowledge within a unified framework, this book will be indispensable to students, educators, and researchers interested in quantum science's profound mysteries and applications.

Abstract

This book delves into the burgeoning field of quantum resource theories, a novel and vibrant area of research within quantum information science that seeks to unify diverse quantum phenomena under a single framework. By recognizing various attributes of physical systems as "resources," this approach offers a fresh perspective on quantum phenomena, transforming our understanding and application of concepts such as quantum entanglement, coherence, and more. With a focus on the pedagogical, the book aims to equip readers with the advanced mathematical tools and physical principles needed to navigate and contribute to this rapidly evolving field. It covers a wide range of topics, from the foundational aspects of quantum mechanics and quantum information to detailed explorations of specific resource theories, including entanglement, asymmetry, and thermodynamics. Through rigorous mathematical exposition and a unique axiomatic approach, the book provides deep insights into the operational and conceptual frameworks that underpin quantum resource theories, making it an invaluable resource for graduate students, early-career researchers, and anyone interested in the cutting-edge developments in quantum information science.

Resources of the Quantum World

TL;DR

Providing the latest developments in the field as well as established knowledge within a unified framework, this book will be indispensable to students, educators, and researchers interested in quantum science's profound mysteries and applications.

Abstract

This book delves into the burgeoning field of quantum resource theories, a novel and vibrant area of research within quantum information science that seeks to unify diverse quantum phenomena under a single framework. By recognizing various attributes of physical systems as "resources," this approach offers a fresh perspective on quantum phenomena, transforming our understanding and application of concepts such as quantum entanglement, coherence, and more. With a focus on the pedagogical, the book aims to equip readers with the advanced mathematical tools and physical principles needed to navigate and contribute to this rapidly evolving field. It covers a wide range of topics, from the foundational aspects of quantum mechanics and quantum information to detailed explorations of specific resource theories, including entanglement, asymmetry, and thermodynamics. Through rigorous mathematical exposition and a unique axiomatic approach, the book provides deep insights into the operational and conceptual frameworks that underpin quantum resource theories, making it an invaluable resource for graduate students, early-career researchers, and anyone interested in the cutting-edge developments in quantum information science.
Paper Structure (556 sections, 387 theorems, 3643 equations, 61 figures, 1 table)

This paper contains 556 sections, 387 theorems, 3643 equations, 61 figures, 1 table.

Table of Contents

  1. Introductory Material
  2. Introduction
  3. About This Book
  4. The Structure of the Book
  5. Resurrection of Quantum Entanglement: The Birth of a Fundamental Resource
  6. Quantum Teleportation
  7. Superdense Coding
  8. Resource Analysis and Reversibility
  9. The Coherent Bit Channel
  10. Coherent Superdense Coding
  11. Coherent Teleportation
  12. Notes and References
  13. Preliminaries
  14. Elements of Quantum Mechanics I: Closed Systems
  15. The Stern-Gerlach Experiment
  16. ...and 541 more sections

Key Result

Theorem 2.1

Let $\mathcal{L}(n)\subset\mathcal{P}(n)$ be the set of all local probability vectors as in 0local0 with fixed cardinalities $|X|$, $|Y|$, $|A|$, $|B|$, and $n=|ABXY|$. Then, $\mathbf{p}\not\in\mathcal{L}(n)$ if and only if it violates at least one Bell inequality.

Figures (61)

  • Figure 1: Unification of Resources
  • Figure 2: The Structure of Quantum Resource Theories
  • Figure 3: Quantum teleportation. Single-line arrows correspond to quantum systems. Double line arrows correspond to classical systems.
  • Figure 4: Entanglement Swapping.
  • Figure 5: Superdense Coding. Double-lines corresponds to classical systems, and single lines to quantum systems.
  • ...and 56 more figures

Theorems & Definitions (984)

  • Definition 2.1
  • Remark
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Remark
  • Definition 2.5
  • Definition 2.6
  • Theorem 2.1
  • Definition 3.1
  • ...and 974 more