Quantum Information References
Quantum information has its own notation, priorities, and proof culture. It overlaps with ordinary quantum mechanics through density matrices, measurements, tensor products, and unitary dynamics, but it often asks different questions: communication, computation, distinguishability, cryptography, error correction, and resource conversion.
Use this page with the Quantum Information Roadmap, the quantum information formula pages, and the Density Matrix Convention Translator.
Best First Reference
Section titled “Best First Reference”Nielsen and Chuang, Quantum Computation and Quantum Information.
Best for: the standard broad entry point into qubits, gates, circuits, density matrices, quantum channels, algorithms, error correction, and information-theoretic language.
Watch for: some notation and examples reflect the state of the field at the book’s major editions. Use more recent references for hardware thresholds, fault-tolerant resource estimates, and device-specific claims.
Mathematical Quantum Information
Section titled “Mathematical Quantum Information”Watrous, The Theory of Quantum Information.
Best for: channels, measurements, norms, semidefinite programming, entanglement, nonlocal games, and theorem-level quantum information.
Watch for: it is mathematically polished and assumes comfort with linear algebra and proof-based reasoning.
Holevo, Quantum Systems, Channels, Information.
Best for: mathematically mature treatment of quantum statistical models, channels, capacities, and continuous-variable aspects.
Watch for: notation and emphasis differ from computer-science-oriented quantum computing texts.
Hayashi, Quantum Information Theory.
Best for: asymptotic information theory, hypothesis testing, channel coding, and statistical structure.
Watch for: it is not the fastest route into algorithms or circuit models.
Computation and Algorithms
Section titled “Computation and Algorithms”Kitaev, Shen, and Vyalyi, Classical and Quantum Computation.
Best for: complexity-theoretic structure, quantum algorithms, and the mathematical computer-science side of quantum computation.
Watch for: it is terse and assumes significant mathematical maturity.
Preskill, quantum computation lecture notes.
Best for: error correction, fault tolerance, stabilizers, entropy, and graduate-level conceptual organization.
Watch for: cite a stable version or section when using lecture notes as a source for a technical statement.
Gottesman, stabilizer formalism thesis.
Best for: stabilizer codes, Clifford operations, and the foundations of a central quantum error-correction language.
Watch for: later books and reviews may be better for current threshold and architecture claims.
Entanglement and Nonlocality
Section titled “Entanglement and Nonlocality”Horodecki et al., “Quantum entanglement.”
Best for: taxonomy of entanglement measures, separability criteria, distillation, and multipartite structure.
Watch for: it is a major review, not a substitute for current specialized papers on platform-specific entanglement certification.
Brunner et al., “Bell nonlocality.”
Best for: Bell inequalities, nonlocal games, device-independent reasoning, and the conceptual bridge from foundations to information.
Watch for: historical Bell-test status and device-independent technology require later sources for current claims.
Convention Checks
Section titled “Convention Checks”- Logs may use base , base , or unspecified units; entropy formulas must state the convention.
- Channels may be written in Schrödinger picture on states or Heisenberg picture on observables.
- Choi matrices depend on vectorization and transpose conventions.
- Tensor-factor order matters in circuit notation and partial traces.
- Fidelity and trace distance have closely related but nonidentical normalization conventions.
Cross-Links
Section titled “Cross-Links”- Quantum Information Roadmap
- Quantum Gates
- Density Matrix Expectation
- Partial Trace
- Quantum Information Problem Map
References
Section titled “References”- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th anniversary ed., Cambridge University Press, 2010.
- J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018; online version: https://cs.uwaterloo.ca/~watrous/TQI/.
- A. S. Holevo, Quantum Systems, Channels, Information: A Mathematical Introduction, De Gruyter, 2012.
- M. Hayashi, Quantum Information Theory: Mathematical Foundation, 2nd ed., Springer, 2017.
- A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi, Classical and Quantum Computation, American Mathematical Society, 2002.
- J. Preskill, Lecture Notes for Quantum Computation, Caltech.
- D. Gottesman, “Stabilizer Codes and Quantum Error Correction,” Ph.D. thesis, Caltech, 1997, arXiv: quant-ph/9705052.
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Reviews of Modern Physics 81, 865-942 (2009), DOI: 10.1103/RevModPhys.81.865.
- N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of Modern Physics 86, 419-478 (2014), DOI: 10.1103/RevModPhys.86.419.