Table of contents

Naimark Dilation from First Principles

A rigorous undergraduate path from Hilbert spaces and POVMs to the proof and quantum information applications

Read each section in order. Every title can be opened as a TheoryTrace document.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: The Measurement Problem in Quantum Information
• Chapter 2: Linear Algebra for Quantum Theory
• Chapter 3: Hilbert Spaces and Operators
• Chapter 4: Quantum States
• Chapter 5: Projective Measurements
• Chapter 6: From Projective Measurements to POVMs
• Chapter 7: Probability, Positivity, and the Born Rule for POVMs
• Chapter 8: Ancillas and Enlarged Quantum Systems
• Chapter 9: Isometries, Embeddings, and Dilations
• Chapter 10: Statement of Naimark's Dilation Theorem
• Chapter 11: The Finite-Dimensional Proof
• Chapter 12: Understanding the Construction
• Chapter 13: Minimal Dilations and Uniqueness
• Chapter 14: Measurement Operators and Instruments
• Chapter 15: Naimark Dilation via Unitary Interaction
• Chapter 16: Relation to Stinespring Dilation
• Chapter 17: Examples of POVM Dilations
• Chapter 18: Quantum State Discrimination
• Chapter 19: Quantum Communication and Information Extraction
• Chapter 20: Quantum Cryptography and Security
• Chapter 21: Quantum Tomography and Experimental Measurement
• Chapter 22: Infinite-Dimensional and Measure-Theoretic Outlook
• Chapter 23: Common Pitfalls and Proof Techniques
• Chapter 24: Capstone: Building and Using a Naimark Dilation
• Conclusion