Book contents
- Classical and Quantum Information Theory
- Reviews
- Classical and Quantum Information Theory
- Copyright page
- Contents
- Preface
- Acknowledgments
- Notations
- Acronyms
- Part I Classical Information
- Part II Quantum Information
- Part III Dynamic Information
- Part IV Bipartite Classical Information
- Part V Bipartite Quantum Information
- Part VI Multipartite Classical and Quantum Information
- Postface
- Index
- References
Part I - Classical Information
Published online by Cambridge University Press: 16 February 2026
Book contents
- Classical and Quantum Information Theory
- Reviews
- Classical and Quantum Information Theory
- Copyright page
- Contents
- Preface
- Acknowledgments
- Notations
- Acronyms
- Part I Classical Information
- Part II Quantum Information
- Part III Dynamic Information
- Part IV Bipartite Classical Information
- Part V Bipartite Quantum Information
- Part VI Multipartite Classical and Quantum Information
- Postface
- Index
- References
Information
- Type
- Chapter
- Information
- Classical and Quantum Information TheoryUncertainty, Information, and Correlation, pp. 1 - 156Publisher: Cambridge University PressPrint publication year: 2026
References
References
Taleb, N. N., Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. New York: Random House, 2005.Google Scholar
Thompson, E., Escape from Model Land: How Mathematical Models Can Lead Us Astray and What We Can Do About It. London: Basic Books, 2022.Google Scholar
Aczél, J. and Daróczy, Z., On Measures of Information and Their Characterizations. New York: Academic Press, 1975.Google Scholar
Polyanskiy, Y. and Wu, Y., Information Theory: From Coding to Learning. Cambridge: Cambridge University Press, 2024.CrossRefGoogle Scholar
Egginton, W., The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality. New York: Pantheon, 2023.Google Scholar
References
Cover, T. M. and Thomas, J. A., Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley-Interscience, 2006.Google Scholar
Kontoyiannis, I. and Verdú, S., “Optimal lossless data compression: Non-asymptotics and asymptotics,” IEEE Transactions on Information Theory, vol. 60, no. 2, pp. 777–795, 2013.Google Scholar
Hart, S., Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature. New York: Flatiron Books, 2023.Google Scholar
Oppenheim, J., Horodecki, M., Horodecki, P., and Horodecki, R., “Thermodynamical approach to quantifying quantum correlations,” Physical Review Letters, vol. 89, no. 18, art. 180402, 2002.CrossRefGoogle ScholarPubMed
Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen, A., Sen, U., and Synak-Radtke, B., “Local versus nonlocal information in quantum-information theory: Formalism and phenomena,” Physical Review A, vol. 71, no. 6, art. 062307, 2005.CrossRefGoogle Scholar
Boyd, S. and Vandenberghe, L., Convex Optimization. Cambridge: Cambridge University Press, 2004.CrossRefGoogle Scholar
References
Tibshirani, R., “Statistical learning theory.” https://www.stat.berkeley.edu/ryantibs/statlearn-s23/, 2023, University of California, Berkeley, Department of Statistics.Google Scholar
Touchette, H., “When is a quantity additive, and when is it extensive?” Physica A: Statistical Mechanics and its Applications, vol. 305, no. 1–2, pp. 84–88, 2002.CrossRefGoogle Scholar
Jensen, H. J., Complexity Science: The Study of Emergence. Cambridge: Cambridge University Press, 2022.CrossRefGoogle Scholar
Golomb, S., “The information generating function of a probability distribution (corresp.),” IEEE Transactions on Information Theory, vol. 12, no. 1, pp. 75–77, 1966.CrossRefGoogle Scholar
Futami, F., Sato, I., and Sugiyama, M., “Expectation propagation for t-exponential family using q-algebra,” Advances in Neural Information Processing Systems, vol. 30, 2017.Google Scholar
Tyagi, H. and Watanabe, S., Information-Theoretic Cryptography. Cambridge: Cambridge University Press, 2023.CrossRefGoogle Scholar
Wilming, H., Goihl, M., Roth, I., and Eisert, J., “Entanglement-ergodic quantum systems equilibrate exponentially well,” Physical Review Letters, vol. 123, no. 20, art. 200604, 2019.CrossRefGoogle ScholarPubMed
Bengtsson, I. and Życzkowski, K., Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge: Cambridge University Press, 2017.CrossRefGoogle Scholar
Boyd, S. and Vandenberghe, L., Convex Optimization. Cambridge: Cambridge University Press, 2004.CrossRefGoogle Scholar
Amigó, J. M., Balogh, S. G., and Hernández, S., “A brief review of generalized entropies,” Entropy, vol. 20, no. 11, p. 813, 2018.CrossRefGoogle ScholarPubMed
Nielsen, F., “What is … an inductive mean?” Notices of the American Mathematical Society, vol. 70, no. 11, p. 1, 2023. [Online]. Available at: http://dx.doi.org/10.1090/noti2832CrossRefGoogle Scholar
Arıkan, E., “Guessing and cryptography 1,” Aspects of Network and Information Security, vol. 17, p. 211, 2008.Google Scholar
Campbell, L. L., “A coding theorem and Rényi’s entropy,” Information and Control, vol. 8, no. 4, pp. 423–429, 1965.CrossRefGoogle Scholar
Aczél, J. and Daróczy, Z., On Measures of Information and Their Characterizations. New York: Academic Press, 1975.Google Scholar
References
Simeone, O., Machine Learning for Engineers. Cambridge: Cambridge University Press, 2022.CrossRefGoogle Scholar
Tyagi, H. and Watanabe, S., Information-Theoretic Cryptography. Cambridge: Cambridge University Press, 2023.CrossRefGoogle Scholar
Farquhar, S., Kossen, J., Kuhn, L., and Gal, Y., “Detecting hallucinations in large language models using semantic entropy,” Nature, vol. 630, no. 8017, pp. 625–630, 2024.CrossRefGoogle ScholarPubMed
Cichocki, A. and Amari, S.-i., “Families of alpha- beta- and gamma-divergences: Flexible and robust measures of similarities,” Entropy, vol. 12, no. 6, pp. 1532–1568, 2010.CrossRefGoogle Scholar
Cover, T. M. and Thomas, J. A., Elements of Information Theory. New York: Wiley, 2006.Google Scholar
Kay, S. M., Information-Theoretic Signal Processing and its Applications. Independently published, 2020.Google Scholar
Saha, S. and Kayal, S., “General weighted information and relative information generating functions with properties,” IEEE Transactions on Information Theory, vol. 70, no. 8, pp. 5498–5515, 2024.CrossRefGoogle Scholar
Van Erven, T. and Harremos, P., “Rényi divergence and Kullback–Leibler divergence,” IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 3797–3820, 2014.CrossRefGoogle Scholar
Polyanskiy, Y. and Wu, Y., Information Theory: From Coding to Learning. Cambridge: Cambridge University Press, 2024.CrossRefGoogle Scholar
Gilardoni, G. L., “On Pinsker’s and Vajda’s type inequalities for Csiszár’s f-divergences,” IEEE Transactions on Information Theory, vol. 56, no. 11, pp. 5377–5386, 2010.CrossRefGoogle Scholar
Chewi, S., Niles-Weed, J., and Rigollet, P., “Statistical optimal transport,” arXiv, 2024. [Online]. Available at: https://arxiv.org/abs/2407.18163Google Scholar
Accessibility standard: WCAG 2.0 A
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this book
conforms to version 2.0 of the
Web Content Accessibility Guidelines
(WCAG), ensuring core accessibility principles are addressed and meets the basic
(A)
level of WCAG compliance, addressing essential accessibility barriers.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
Structural and Technical Features
ARIA roles provided
You gain clarity from ARIA (Accessible Rich Internet Applications) roles and attributes, as they help assistive technologies interpret how each part of the content functions.
You gain clarity from ARIA (Accessible Rich Internet Applications) roles and attributes, as they help assistive technologies interpret how each part of the content functions.