MODERN QUANTUM THEORY: FROM QUANTUM MECHANICS TO ENTANGLEMENT AND QUANTUM INFORMATION

PART I - QUANTUM MECHANICS
1:Wave-Particle Duality
2:The Time-Dependent Schrödinger Equation
3:Mathematical Formalism of Quantum Mechanics
4:The Time-Independent Schrödinger Equation
5:The Quantum Harmonic Oscillator
6:Orbital Angular Momentum
7:The Three-Dimensional Schrödinger Equation
8:Spin and Atomic Structure
9:Electromagnetism in Quantum Mechanics
10:Perturbative Methods in Quantum Mechanics
PART II - ENTANGLEMENT AND NON-LOCALITY
11:Density Matrices
12:Hidden-Variable Theories
13:Bell Inequalities
14:Quantum Teleportation
15:Entanglement and Separability
16:Quantification and Conversion of Entanglement
17:High-Dimensional Quantum Systems
18:Multipartite Entanglement
PART III - ADVANCED TOPICS IN MODERN QUANTUM PHYSICS
19:Entropy of Classical Systems
20:Quantum Entropy and Correlations in Quantum Information
21:Quantum Channels and Quantum Operations
22:Open Quantum Systems, Decoherence, Atom-Field Coupling
23:Quantum Measurements
24:Quantum Metrology
25:Quantum States of Light
26:Particle Physics - Bell Inequalities
27:Particle Physics - Entanglement & Decoherence

In the last few decades quantum theory has experienced an extensive revival owing to the rapid development of quantum information and quantum technologies. Based on a series of courses taught by the authors, the book takes the reader on a journey from the beginnings of quantum theory in the early twentieth century to the realm of quantum-information processing in the twenty-first. The central aim of this textbook, therefore, is to offer a detailed introduction to quantum theory that covers both physical and information-theoretic aspects, with a particular focus on the concept of entanglement and its characteristics, variants, and applications.

Suitable for undergraduate students in physics and related subjects who encounter quantum mechanics for the first time, this book also serves as a resource for graduate students who want to engage with more advanced topics, offering a collection of derivations, proofs, technical methods, and references for graduate students and more experienced readers engaged with teaching and active research.

The book is divided into three parts: Part I - Quantum Mechanics, Part II - Entanglement and Non-Locality, and Part III - Advanced Topics in Modern Quantum Physics. Part I provides a modern view on quantum mechanics, a central topic of theoretical physics. Part II is dedicated to the foundations of quantum mechanics and entanglement: starting with density operators, hidden-variable theories, the Einstein-Podolsky-Rosen Paradox, and Bell Inequalities, but also touching upon philosophical questions, followed by a deeper study of entanglement-based quantum communication protocols like teleportation, before giving a detailed exposition of entanglement theory, including tools for the detection and quantification of entanglement. Part III is intended as a collection of standalone chapters to supplement the contents of Parts I and II, covering more advanced topics such as classical and quantum entropies, quantum operations and measurements, decoherence, quantum metrology and quantum optics, and entanglement in particle physics.