Quantum Theory from First Principles: An Informational Approach

by Giacomo Mauro D'Ariano, Giulio Chiribella, Paolo Perinotti

Overview

Quantum theory is the soul of theoretical physics. It is not just a theory of specific physical systems, but rather a new framework with universal applicability. This book shows how we can reconstruct the theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up. Step by step, the reader will learn how to master the counterintuitive aspects of the quantum world, and how to efficiently reconstruct quantum information protocols from first principles. Using intuitive graphical notation to represent equations, and with shorter and more efficient derivations, the theory can be understood and assimilated with exceptional ease. Offering a radically new perspective on the field, the book contains an efficient course of quantum theory and quantum information for undergraduates. It is aimed at researchers, professionals, and students in physics, computer science and philosophy, as well as the curious outsider seeking a deeper understanding of the theory.

Product Details

ISBN-13:	9781107043428
Publisher:	Cambridge University Press
Publication date:	01/28/2017
Pages:	356
Product dimensions:	7.64(w) x 9.96(h) x 0.91(d)

About the Author

Giacomo Mauro D'Ariano is a Professor at Università degli Studi di Pavia, Italy, where he teaches quantum mechanics and foundations of quantum theory, and leads the Quantum Information Theory (QUIT) group. He is a Fellow of the American Physical Society and of the Optical Society of America, a member of the Academy Istituto Lombardo of Scienze e Lettere, the Center for Photonic Communication and Computing at Northwestern University, Illinois, and the Foundational Questions Institute (FQXi).

Giulio Chiribella is Associate Professor in the Department of Computer Science at The University of Hong Kong. He is a Visiting Fellow of Perimeter Institute for Theoretical Physics, a member of the Standing Committee of the International Colloquia on Group Theoretical Methods in Physics, and a member of the Foundational Questions Institute (FQXi). In 2010, he was awarded the Hermann Weyl Prize for applications of group theory in quantum information.

Paolo Perinotti is Assistant Professor at Università degli Studi di Pavia, Italy, where he teaches quantum information theory. His research activity is focused on foundations of quantum information, quantum mechanics and quantum field theory. He is a member of the Foundational Questions Institute (FQXi) and the International Quantum Structures Association. In 2016 he was awarded the Birkhoff-von Neumann Prize for research in quantum foundations.

Table of Contents

Preface; Acknowledgments; 1. Introduction; Part I. The Status Quo: 2. Quantum theory from Hilbert-spaces; Part II. The Informational Approach: 3. The framework; 4. The new principles; 5. Causal theories; 6. Theories with local discriminability; 7. The purification principle; Part III. Quantum Information without Hilbert Spaces: 8. Encoding information; 9. Three no-go theorems; 10. Perfectly discriminable states; 11. Identifying pure states; 12. Diagonalization; Part IV. Quantum Theory from the Principles: 13. Conclusive teleportation; 14. The qubit; 15. Projections; 16. The superposition principle; 17. Derivation of quantum theory; References; Index.

Editorial Reviews

‘An extraordinary book on the deep principles behind quantum theory.' Nicolas Gisin, Université de Genève

‘Part quantum mechanics textbook, part original research contribution, this book is a fascinating, audacious effort to ‘rebuild quantum mechanics from the ground up', presenting it as the logical consequence of simple information-theoretic postulates. Students wishing to learn quantum information should read it and do all the exercises!' Scott Aaronson, Massachusetts Institute of Technology

'From the earliest days of quantum theory to the present, physicists have been pleased with the excellent results it yields but also unsettled (in varying degrees) by the fact that its mathematical forms do not always have clear physical interpretations. Some efforts to resolve this problem in recent decades have focused on replacing mathematical postulates with informational postulates. The authors take this approach here … [intended for] not just physicists but also mathematicians and computer scientists. The first section, about one-third of the book's length, is flagged by the authors as suitable for an undergraduate course and might well serve so at the highest undergraduate levels … The two remaining sections are aimed at a master's-level audience; the final section lays out the derivation of quantum theory from six informational principles … A generous number (more than 200) practice exercises are included, with solutions available for selected problems.' K. D. Fisher, Choice

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