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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.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: The Measurement Problem in Quantum Information5
- Chapter 2: Linear Algebra for Quantum Theory6
- Chapter 3: Hilbert Spaces and Operators7
- Chapter 4: Quantum States8
- Chapter 5: Projective Measurements9
- Chapter 6: From Projective Measurements to POVMs10
- Chapter 7: Probability, Positivity, and the Born Rule for POVMs11
- Chapter 8: Ancillas and Enlarged Quantum Systems12
- Chapter 9: Isometries, Embeddings, and Dilations13
- Chapter 10: Statement of Naimark's Dilation Theorem14
- Chapter 11: The Finite-Dimensional Proof15
- Chapter 12: Understanding the Construction16
- Chapter 13: Minimal Dilations and Uniqueness17
- Chapter 14: Measurement Operators and Instruments18
- Chapter 15: Naimark Dilation via Unitary Interaction19
- Chapter 16: Relation to Stinespring Dilation20
- Chapter 17: Examples of POVM Dilations21
- Chapter 18: Quantum State Discrimination22
- Chapter 19: Quantum Communication and Information Extraction23
- Chapter 20: Quantum Cryptography and Security24
- Chapter 21: Quantum Tomography and Experimental Measurement25
- Chapter 22: Infinite-Dimensional and Measure-Theoretic Outlook26
- Chapter 23: Common Pitfalls and Proof Techniques27
- Chapter 24: Capstone: Building and Using a Naimark Dilation28
- Conclusion29