Selected references to topics in mathematics and quantum information theory

On this page I am collecting selected references to topics in mathematics and quantum information theory that intersect with my own research interests. I compiled these lists having graduate students in mind who want to start working on questions related to these topics. Hopefully, they are also useful for more experienced researchers.

List of lists

How to navigate these lists

I've tried to indicate the difficulty of the material using three levels: B Beginner M Medium A Advanced
Note that this is a rough and very subjective classification, and only meant to provide some rudimentary guidelines for how to navigate the material.

Please get in touch with me if you have any questions on how to start with these topics, or if I have forgotten any resources you think should be included!

Representation theory and its applications in quantum information theory

General representation theory

Fulton, Harris: Representation theory: A first course (textbook) B M
Serre: Linear representations of finite groups (textbook) M
Teleman: Representation theory (lecture notes) M

Representation theory of the symmetric group

Audenaert: A digest on representation theory of the symmetric group (survey, copy available on request) M
Christandl: The structure of bipartite quantum states - Insights from group theory and cryptography (PhD thesis) B M
James: The representation theory of the symmetric groups (textbook) M
Zhao: Young Tableaux and the representations of the symmetric group (student article) B
🠕 [FH]

Representation theory of Lie groups and Lie algebras

Čap: Lie algebras and representation theory (lecture notes) B M
Čap: Lie groups (lecture notes) B M
Carter, Segal, MacDonald: Lectures on Lie Groups and Lie Algebras (textbook) B M
Itzykson, Nauenberg: Unitary Groups: Representations and Decompositions (review article) B M
Procesi: Lie Groups - An approach through Invariants and Representations (textbook) M
🠕 [Ch]
🠕 [FH]

Schur-Weyl duality

Harrow: Applications of coherent classical communication and the Schur transform to quantum information theory (PhD thesis) B M
Walter: Symmetry and Quantum Information (lecture notes) B
🠕 [Ch]

Selected applications of representation theory in quantum information theory

Christandl et al.: One-and-a-half quantum de Finetti theorems (research article) A
Christandl, Koenig, Renner: Post-selection technique for quantum channels with applications to quantum cryptography (research article) M
Christandl, Schuch, Winter: Entanglement of the antisymmetric state (research article) A
Gross, Nezami, Walter: Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations (research article) A
Haah et al.: Sample-optimal tomography of quantum states (research article) A
Harrow: The Church of the Symmetric Subspace (review article) B
Keyl, Werner: Optimal Cloning of Pure States, Judging Single Clones (research article) M
Keyl, Werner: Estimating the spectrum of a density operator (research article) M
Leditzky: Optimality of the pretty good measurement for port-based teleportation (research article) M
Mozrzymas et al.: Optimal Port-based Teleportation (research article) A
O'Donnell: Learning and Testing Quantum States via Probabilistic Combinatorics and Representation Theory (survey) B
🠕 [Ch]
🠕 [Ha1]
🠕 [Wa]

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