Quantum Theory from First Principles
An Informational Approach

A new presentation of quantum theory and quantum information based on fundamental principles, for anyone seeking a deeper understanding of the subject.

Giacomo Mauro D'Ariano (Author), Giulio Chiribella (Author), Paolo Perinotti (Author)

9781108714419, Cambridge University Press

Paperback / softback, published 6 June 2019

358 pages, 20 b/w illus.
24.5 x 19 x 2 cm, 0.6 kg

'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

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.

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.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], History of science [PDX], Philosophy of science [PDA]