The Theory of Quantum Information
Abstract
This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.
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In quantum theory, global isometries suffice (captured by Stinespring dilation); classical theory requires the use of auxiliary randomness.
“In quantum theory, global isometries suffice (captured by a Stinespring dilation [54]); however, classical theory requires the use of auxiliary randomness [53].”
From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [54]
Some procedures have been proposed in the literature to derive Kraus operators from the underlying quantum Markovian master equation.
“Nonetheless, some procedures have been proposed in the literature [62, 63].”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [63]
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Efficient quantum measurement of Pauli operators in the presence of finite sampling error
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Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage
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Fisher-information susceptibility for multiparameter quantum estimation
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Simple formulation of no-cloning and no-hiding that admits efficient and robust verification
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“In quantum theory, global isometries suffice (captured by a Stinespring dilation [54]), however classical theory requires the use of auxiliary randomness [53].”
- Authors
- Watrous, J.
- Affiliations
- University of Waterloo (CA)
- Corresponding author
- Watrous, John
- ORCID
- Watrous, John
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2018-04-26
- OpenAlex
- W2804172638
- Semantic Scholar
- 60f64eb4d2223f4ab3d320e926d927c41da8bfb9
- Cited by
- 1,325
- References
- 195
- Citations by year
- 2026: 126 · 2025: 206 · 2024: 176 · 2023: 132 · 2022: 136 · 2021: 158 · 2020: 140 · 2019: 125 · 2018: 57 · 2017: 29 · 2016: 16 · 2015: 4 · 2014: 7 · 2013: 2 · 2012: 3
- FWCI
- 41.79
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- International Linear Collider (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum information, quantum computing, quantum channels, quantum entanglement, quantum hypothesis testing
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