Classical and Quantum Information Theory
Classical and Quantum Information Theory
Description
The upcoming textbook Classical and Quantum Information Theory by Osvaldo Simeone, © 2025 Simeone to be published on Cambridge University Press offers a comprehensive introduction to classical and quantum information theory. The text progressively increases in complexity from basic measures to advanced quantum information measures, with chapters alternating between classic and quantum systems. It can be used for senior undergraduate and graduate students in electrical engineering, computer science, and applied mathematics, looking to master the essentials of information theory.
Full draft (unedited)
Podcast generated by Google NotebookLM on the first two parts of the book
Table of Content
1. Uncertainty, Information, and Entropy
1.1 Overview
1.2 Uncertainty and Information
1.3 System, States, and Informational State
1.4 Uncertainty and Entropy
1.5 Axiomatic vs. Operational Definitions of Entropy
1.6 Summary
1.7 Recommended Resources
2. Information Quantification by Asking or Compressing or Sampling: Shannon Entropy
2.1 Overview
2.2 Quantifying Information by Asking
2.3 Huffman Code
2.4 Ideal Codeword Lengths and Shannon Surprise
2.5 Shannon Entropy
2.6 Quantifying Information by Compressing
2.7 Quantifying Information as Randomness for Sampling
2.8 Summary
2.9 Recommended Resources
3. Information Quantification by Predicting or Guessing: Tsallis Entropy and Rényi Entropy
3.1 Overview
3.2 Information Quantification by Predicting
3.3 α-Log-Loss
3.4 Tsallis Entropy
3.5 Quantifying Information by Guessing
3.6 Rényi Entropy
3.7 Compression Beyond Average Codeword Length
3.8 Unifying Entropies
3.9 Summary
3.10 Recommended Resources
4. Relative Entropy
4.1 Overview
4.2 Shannon Relative Entropy
4.3 Monotonicity of the Shannon Entropy
4.4 Tsallis Relative Entropy and Its Monotonicity
4.5 Fidelity
4.6 Summary
4.7 Recommended Resources
5. From Classical to Quantum Information
5.1 Overview
5.2 Classical vs. Quantum Information
5.3 Quantum Measurement and Superposition
5.4 Contextuality
5.5 Quantum Uncertainty
5.6 Summary
5.7 Recommended Resources
6. Quantum Uncertainty and Coherence
6.1 Overview
6.2 Quantum Uncertainty Measures
6.3 Coherence and Basis Dependence
6.4 Compatibility and the Uncertainty Principle
6.5 Projective Measurements
6.6 Normal Matrices and the Spectral Theorem
6.7 Summary
6.8 Recommended Resources
7. Classical and Quantum Uncertainty: Mixed States and Quantum Entropy
7.1 Overview
7.2 Ensembles and Density Matrices
7.3 Projective Measurements of Mixed States
7.4 Uncertainty Inequalities for Observables
7.5 Quantum Entropy
7.6 Summary
7.7 Recommended Resources
8. Quantum Relative Information
8.1 Overview
8.2 Quantum Relative Entropies
8.3 Fidelity Between Mixed States
8.4 Rényi Quantum Relative Entropy
8.5 Detection, Trace Distance, and Information
8.6 Purification
8.7 Kronecker Product and Quantum Information
8.8 Summary
8.9 Recommended Resources
9. Classical Dynamic Information
9.1 Overview
9.2 Random Shuffling
9.3 Majorization
9.4 Schur Concavity
9.5 Channels and Data Processing Inequality
9.6 Summary
9.7 Recommended Resources
10. Quantum Dynamic Information in Closed Systems
10.1 Overview
10.2 Unitary Transformations
10.3 Interpreting Unitaries
10.4 Quantum Information Dynamics
10.5 Summary
10.6 Recommended Resources
11. Quantum Dynamic Information in Open Systems
11.1 Overview
11.2 Random Unitary Evolution
11.3 Quantum Channels and POVMs
11.4 Quantum Instruments
11.5 Summary
11.6 Recommended Resources
12. Bipartite Classical Information as Correlation
12.1 Overview
12.2 Joint and Marginal Distributions
12.3 Mutual Information
12.4 Common and Distillable Information
12.5 Summary
12.6 Recommended Resources
13. Bipartite Classical Information via Residual Uncertainty
13.1 Overview
13.2 Conditional Distributions and Ensemble Entropy
13.3 Locally Accessible Information
13.4 Conditional Entropy and Fano’s Inequality
13.5 Summary
13.6 Recommended Resources
14. Bipartite Classical and Quantum Information for Pure States
14.1 Overview
14.2 Bipartite Quantum Pure States
14.3 Entanglement and Superposition
14.4 Local Measurements and Reduced Density Matrices
14.5 Classical and Quantum Correlation Measures
14.6 Summary
14.7 Recommended Resources
15. Bipartite Dynamic Quantum and Classical Information for Pure States
15.1 Overview
15.2 Entanglement Generation and LOCC
15.3 Entanglement Monotones
15.4 Operational Tasks and Entanglement Transformation
15.5 Summary
15.6 Recommended Resources
16. Bipartite Dynamic Quantum and Classical Information for Mixed States
16.1 Overview
16.2 Classical-Classical and Classical-Quantum States
16.3 Separability and Discord
16.4 Entanglement Detection
16.5 Summary
16.6 Recommended Resources
17. A Brief Introduction to Tensor Networks
17.1 Overview
17.2 Tensor Definitions and Operations
17.3 Tensor Products and Contractions
17.4 Matrix Representation and Partial Trace
17.5 Vectorization and Matrization
17.6 Summary
17.7 Recommended Resources
18. Multipartite Classical Information – Fragmentation, Scale, and Strength
18.1 Overview
18.2 Measures of Correlation and Mutual Information
18.3 Conditional Mutual Information
18.4 Fragmentation Measures
18.5 Strength and Scale of Correlation
18.6 Summary
18.7 Recommended Resources
19. Multipartite Classical Information – Structure
19.1 Overview
19.2 Conditional Mutual Information
19.3 Markov Networks
19.4 Latent Variable Models
19.5 Summary
19.6 Recommended Resources
20. Multipartite Quantum Information – Fragmentation, Scale, and Strength
20.1 Overview
20.2 Globally vs. Locally Entangled States
20.3 Entanglement Classes and Canonical Form
20.4 Summary
20.5 Recommended Resources
21. Multipartite Quantum Information – Structure
21.1 Overview
21.2 Matrix Product States
21.3 Quantum Circuits
21.4 ZX Calculus
21.5 Summary
21.6 Recommended Resources
Cite as: O. Simeone, ``Classical and Quantum Information Theory,'' to appear, Cambridge University Press (https://sites.google.com/view/osvaldosimeone/cqit). [@misc{simeone_cqit, author = {Simeone, Osvaldo}, title = {Classical and Quantum Uncertainty, Information, and Correlation}, note = {In preparation}, howpublished = {\url{https://sites.google.com/view/osvaldosimeone/cqit}}, year = {2024} }]
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