On Graph Approaches to Contextuality and their Role in Quantum Theory

On Graph Approaches to Contextuality and their Role in Quantum Theory

Author: Barbara Amaral

Publisher: Springer

Published: 2018-07-28

Total Pages: 135

ISBN-13: 3319938274

DOWNLOAD EBOOK

This book explores two of the most striking features of quantum theory – contextuality and nonlocality – using a formulation based on graph theory. Quantum theory provides a set of rules to predict probabilities of different outcomes in different experimental settings, and both contextuality and nonlocality play a fundamental role in interpreting the outcomes. In this work, the authors highlight how the graph approach can lead to a better understanding of this theory and its applications. After presenting basic definitions and explaining the non-contextuality hypothesis, the book describes contextuality scenarios using compatibility hypergraphs. It then introduces the exclusivity graph approach, which relates a number of important graph-theoretical concepts to contextuality. It also presents open problems such as the so-called Exclusivity Principle, as well as a selection of important topics, like sheaf-theoretical approach, hypergraph approach, and alternative proofs of contextuality.


Book Synopsis On Graph Approaches to Contextuality and their Role in Quantum Theory by : Barbara Amaral

Download or read book On Graph Approaches to Contextuality and their Role in Quantum Theory written by Barbara Amaral and published by Springer. This book was released on 2018-07-28 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores two of the most striking features of quantum theory – contextuality and nonlocality – using a formulation based on graph theory. Quantum theory provides a set of rules to predict probabilities of different outcomes in different experimental settings, and both contextuality and nonlocality play a fundamental role in interpreting the outcomes. In this work, the authors highlight how the graph approach can lead to a better understanding of this theory and its applications. After presenting basic definitions and explaining the non-contextuality hypothesis, the book describes contextuality scenarios using compatibility hypergraphs. It then introduces the exclusivity graph approach, which relates a number of important graph-theoretical concepts to contextuality. It also presents open problems such as the so-called Exclusivity Principle, as well as a selection of important topics, like sheaf-theoretical approach, hypergraph approach, and alternative proofs of contextuality.

Quantum Nonlocality

Quantum Nonlocality

Author: Lev Vaidman

Publisher: MDPI

Published: 2019-06-12

Total Pages: 238

ISBN-13: 3038979481

DOWNLOAD EBOOK

This book presents the current views of leading physicists on the bizarre property of quantum theory: nonlocality. Einstein viewed this theory as “spooky action at a distance” which, together with randomness, resulted in him being unable to accept quantum theory. The contributions in the book describe, in detail, the bizarre aspects of nonlocality, such as Einstein–Podolsky–Rosen steering and quantum teleportation—a phenomenon which cannot be explained in the framework of classical physics, due its foundations in quantum entanglement. The contributions describe the role of nonlocality in the rapidly developing field of quantum information. Nonlocal quantum effects in various systems, from solid-state quantum devices to organic molecules in proteins, are discussed. The most surprising papers in this book challenge the concept of the nonlocality of Nature, and look for possible modifications, extensions, and new formulations—from retrocausality to novel types of multiple-world theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.


Book Synopsis Quantum Nonlocality by : Lev Vaidman

Download or read book Quantum Nonlocality written by Lev Vaidman and published by MDPI. This book was released on 2019-06-12 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the current views of leading physicists on the bizarre property of quantum theory: nonlocality. Einstein viewed this theory as “spooky action at a distance” which, together with randomness, resulted in him being unable to accept quantum theory. The contributions in the book describe, in detail, the bizarre aspects of nonlocality, such as Einstein–Podolsky–Rosen steering and quantum teleportation—a phenomenon which cannot be explained in the framework of classical physics, due its foundations in quantum entanglement. The contributions describe the role of nonlocality in the rapidly developing field of quantum information. Nonlocal quantum effects in various systems, from solid-state quantum devices to organic molecules in proteins, are discussed. The most surprising papers in this book challenge the concept of the nonlocality of Nature, and look for possible modifications, extensions, and new formulations—from retrocausality to novel types of multiple-world theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.

Probing the Meaning of Quantum Mechanics

Probing the Meaning of Quantum Mechanics

Author: Diederik Aerts

Publisher: World Scientific Publishing

Published: 2018-11-20

Total Pages: 392

ISBN-13: 9813276908

DOWNLOAD EBOOK

This book provides an interdisciplinary perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, despite its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted interpretation. The novelty of the book comes from the multiple viewpoints and subjects investigated by a group of researchers from Europe and North and South America.


Book Synopsis Probing the Meaning of Quantum Mechanics by : Diederik Aerts

Download or read book Probing the Meaning of Quantum Mechanics written by Diederik Aerts and published by World Scientific Publishing. This book was released on 2018-11-20 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an interdisciplinary perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, despite its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted interpretation. The novelty of the book comes from the multiple viewpoints and subjects investigated by a group of researchers from Europe and North and South America.

Foundations of Quantum Theory

Foundations of Quantum Theory

Author: E.M. Rasel

Publisher: IOS Press

Published: 2019-01-23

Total Pages: 432

ISBN-13: 1614999376

DOWNLOAD EBOOK

This volume provides a summary of the lectures presented at the International School of Physics "Enrico Fermi" on the Foundations of Quantum Theory, organized by the Italian Physical Society in Varenna, Italy from 8-13 July 2016, in collaboration with the Wilhelm und Else Heraeus-Stiftung. It was the first "Enrico Fermi" Summer School on this topic since 1977. Its main goal was to provide an overview of the recent theoretical and experimental developments in an active field of research, the foundations of quantum mechanics. The field is characterized by a dichotomy of unparalleled agreement between theory and experiment on the one hand, and an enormous variety of interpretations of the underlying mathematical formalism on the other hand. This proceedings of the "Enrico Fermi" Summer School of July 2016 contains 21 contributions on a range of topics: the history and interpretations of quantum theory; the principle of complementarity and wave-particle duality; quantum theory from first principles; the reality of the wave function; the concept of the photon; measurement in quantum theory; the interface of quantum theory and general relativity; and quantum optical tests of quantum theory.


Book Synopsis Foundations of Quantum Theory by : E.M. Rasel

Download or read book Foundations of Quantum Theory written by E.M. Rasel and published by IOS Press. This book was released on 2019-01-23 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a summary of the lectures presented at the International School of Physics "Enrico Fermi" on the Foundations of Quantum Theory, organized by the Italian Physical Society in Varenna, Italy from 8-13 July 2016, in collaboration with the Wilhelm und Else Heraeus-Stiftung. It was the first "Enrico Fermi" Summer School on this topic since 1977. Its main goal was to provide an overview of the recent theoretical and experimental developments in an active field of research, the foundations of quantum mechanics. The field is characterized by a dichotomy of unparalleled agreement between theory and experiment on the one hand, and an enormous variety of interpretations of the underlying mathematical formalism on the other hand. This proceedings of the "Enrico Fermi" Summer School of July 2016 contains 21 contributions on a range of topics: the history and interpretations of quantum theory; the principle of complementarity and wave-particle duality; quantum theory from first principles; the reality of the wave function; the concept of the photon; measurement in quantum theory; the interface of quantum theory and general relativity; and quantum optical tests of quantum theory.

Contextuality From Quantum Physics To Psychology

Contextuality From Quantum Physics To Psychology

Author: Ehtibar N Dzhafarov

Publisher: World Scientific

Published: 2015-11-30

Total Pages: 479

ISBN-13: 9814730629

DOWNLOAD EBOOK

The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology.


Book Synopsis Contextuality From Quantum Physics To Psychology by : Ehtibar N Dzhafarov

Download or read book Contextuality From Quantum Physics To Psychology written by Ehtibar N Dzhafarov and published by World Scientific. This book was released on 2015-11-30 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology.

Exploring Quantum Contextuality with Photons

Exploring Quantum Contextuality with Photons

Author: Zheng-Hao Liu

Publisher: Springer Nature

Published:

Total Pages: 170

ISBN-13: 981996167X

DOWNLOAD EBOOK


Book Synopsis Exploring Quantum Contextuality with Photons by : Zheng-Hao Liu

Download or read book Exploring Quantum Contextuality with Photons written by Zheng-Hao Liu and published by Springer Nature. This book was released on with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Graph Theory: Adiabatic Quantum Computing Methods

Graph Theory: Adiabatic Quantum Computing Methods

Author: N.B. Singh

Publisher: N.B. Singh

Published:

Total Pages: 330

ISBN-13:

DOWNLOAD EBOOK

"Graph Theory: Adiabatic Quantum Computing Methods" explores the convergence of quantum computing and graph theory, offering a comprehensive examination of how quantum algorithms can tackle fundamental graph problems. From foundational concepts to advanced applications in fields like cryptography, machine learning, and network analysis, this book provides a clear pathway into the evolving landscape of quantum-enhanced graph algorithms. Designed for researchers, students, and professionals alike, it bridges theoretical insights with practical implementations, paving the way for innovative solutions in computational graph theory.


Book Synopsis Graph Theory: Adiabatic Quantum Computing Methods by : N.B. Singh

Download or read book Graph Theory: Adiabatic Quantum Computing Methods written by N.B. Singh and published by N.B. Singh. This book was released on with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Graph Theory: Adiabatic Quantum Computing Methods" explores the convergence of quantum computing and graph theory, offering a comprehensive examination of how quantum algorithms can tackle fundamental graph problems. From foundational concepts to advanced applications in fields like cryptography, machine learning, and network analysis, this book provides a clear pathway into the evolving landscape of quantum-enhanced graph algorithms. Designed for researchers, students, and professionals alike, it bridges theoretical insights with practical implementations, paving the way for innovative solutions in computational graph theory.

Introduction to Quantum Graphs

Introduction to Quantum Graphs

Author: Gregory Berkolaiko

Publisher: American Mathematical Soc.

Published: 2013

Total Pages: 291

ISBN-13: 0821892118

DOWNLOAD EBOOK

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.


Book Synopsis Introduction to Quantum Graphs by : Gregory Berkolaiko

Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Quantum Probability and Spectral Analysis of Graphs

Quantum Probability and Spectral Analysis of Graphs

Author: Akihito Hora

Publisher: Springer Science & Business Media

Published: 2007-07-05

Total Pages: 384

ISBN-13: 3540488634

DOWNLOAD EBOOK

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.


Book Synopsis Quantum Probability and Spectral Analysis of Graphs by : Akihito Hora

Download or read book Quantum Probability and Spectral Analysis of Graphs written by Akihito Hora and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Fundamentals of Computation Theory

Fundamentals of Computation Theory

Author: Ralf Klasing

Publisher: Springer

Published: 2017-08-28

Total Pages: 432

ISBN-13: 3662557517

DOWNLOAD EBOOK

This book constitutes the refereed proceedings of the 21st International Symposium on Fundamentals of Computation Theory, FCT 2017, held in Bordeaux, France, in September 2017. The 29 revised full papers and 5 invited papers presented were carefully reviewed and selected from 99 submissions. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.


Book Synopsis Fundamentals of Computation Theory by : Ralf Klasing

Download or read book Fundamentals of Computation Theory written by Ralf Klasing and published by Springer. This book was released on 2017-08-28 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Symposium on Fundamentals of Computation Theory, FCT 2017, held in Bordeaux, France, in September 2017. The 29 revised full papers and 5 invited papers presented were carefully reviewed and selected from 99 submissions. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.