## Representation theory and its applications in quantum information theory

### General representation theory

- [FH]
- Fulton, Harris: Representation theory: A first course (textbook) B M
- [Se]
- Serre: Linear representations of finite groups (textbook) M
- [Te]
- Teleman: Representation theory (lecture notes) M

### Representation theory of the symmetric group

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

### Representation theory of Lie groups and Lie algebras

- [Ca1]
- ÄŒap: Lie algebras and representation theory (lecture notes) B M
- [Ca2]
- ÄŒap: Lie groups (lecture notes) B M
- [CSM]
- Carter, Segal, MacDonald: Lectures on Lie Groups and Lie Algebras (textbook) B M
- [IN]
- Itzykson, Nauenberg: Unitary Groups: Representations and Decompositions (review article) B M
- [Pr]
- Procesi: Lie Groups - An approach through Invariants and Representations (textbook) M
- ðŸ • [Ch]
- ðŸ • [FH]

### Schur-Weyl duality

- [Ha1]
- Harrow: Applications of coherent classical communication and the Schur transform to quantum information theory (PhD thesis) B M
- [Wa]
- Walter: Symmetry and Quantum Information (lecture notes) B
- ðŸ • [Ch]

### Selected applications of representation theory in quantum information theory

- [CKM+]
- Christandl et al.: One-and-a-half quantum de Finetti theorems (research article) A
- [CKR]
- Christandl, Koenig, Renner: Post-selection technique for quantum channels with applications to quantum cryptography (research article) M
- [CSW]
- Christandl, Schuch, Winter: Entanglement of the antisymmetric state (research article) A
- [GNW]
- 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
- [HHJ+]
- Haah et al.: Sample-optimal tomography of quantum states (research article) A
- [Ha2]
- Harrow: The Church of the Symmetric Subspace (review article) B
- [KW1]
- Keyl, Werner: Optimal Cloning of Pure States, Judging Single Clones (research article) M
- [KW2]
- Keyl, Werner: Estimating the spectrum of a density operator (research article) M
- [Le]
- Leditzky: Optimality of the pretty good measurement for port-based teleportation (research article) M
- [MSS+]
- Mozrzymas et al.: Optimal Port-based Teleportation (research article) A
- [OD]
- O'Donnell: Learning and Testing Quantum States via Probabilistic Combinatorics and Representation Theory (survey) B
- ðŸ • [Ch]
- ðŸ • [Ha1]
- ðŸ • [Wa]