## Entanglement theory

### Introductory articles and reviews

- [BZ]
- Bengtsson, Zyczkowski: Quantum entanglement (book chapter) B M
- [BCH+]
- Brandao et al.: The Mathematics of Entanglement (lecture notes) B M
- [FVM+]
- Friis et al.: Entanglement Certification − From Theory to Experiment (review article) B M
- [GT]
- Gühne, Toth: Entanglement detection (review article) B M
- [HDE+]
- Hein et al.: Entanglement in Graph States and its Applications (review article) B
- [H^4]
- Horodecki et al.: Quantum entanglement (review article) B M
- [PV]
- Plenio, Virmani: An introduction to entanglement measures (review article) B

### Entanglement measures

- [CW]
- Christandl, Winter: "Squashed Entanglement" - An Additive Entanglement Measure (research article) M
- [LDH+]
- Lancien et al.: Should Entanglement Measures be Monogamous or Faithful? (research article) M
- [Pl]
- Plenio: The logarithmic negativity: A full entanglement monotone that is not convex (research article) B
- [Vi]
- Vidal: Entanglement monotones (research article) M
- [VW1]
- Vidal, Werner: A computable measure of entanglement (research article) B M
- [VW2]
- Vollbrecht, Werner: Entanglement Measures under Symmetry (research article) B M

### Bipartite entanglement

- [DPS1]
- Doherty, Parrilo, Spedalieri: Distinguishing separable and entangled states (research article) M A
- [DPS2]
- Doherty, Parrilo, Spedalieri: A complete family of separability criteria (research article) M A
- [HLW]
- Hayden, Leung, Winter: Aspects of generic entanglement (research article) M A
- [H^2]
- Horodecki, Horodecki: Reduction criterion of separability and limits for a class of protocols of entanglement distillation (research article) M
- [H^3a]
- Horodecki, Horodecki, Horodecki: Separability of Mixed States: Necessary and Sufficient Conditions (research article) M
- [H^3b]
- Horodecki, Horodecki, Horodecki: Mixed-state entanglement and distillation: is there a "bound" entanglement in nature? (research article) M
- [Ra]
- Rains: A semidefinite program for distillable entanglement (research article) A
- [Wo]
- Wolf: Partial Transposition in Quantum Information Theory (PhD thesis) B M A

### Multipartite entanglement

- [DVC]
- Dür, Vidal, Cirac: Three qubits can be entangled in two inequivalent ways (research article) M
- [GT]
- see above ↑
- [HDE+]
- see above ↑
- [VDM]
- Verstraete, Dehaene, De Moor: Normal forms and entanglement measures for multipartite quantum states (research article) A
- [WGE]
- Walter, Gross, Eisert: Multi-partite entanglement (book chapter) B
- [WD+]
- Walter et al.: Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information (research article) M A
- [Ya]
- Yang: A simple proof of monogamy of entanglement (research article) B

## Haar measure and k-designs

### Haar measure essentials

- [Gl]
- Gleason: Existence and uniqueness of Haar measure (lecture notes) B
- [Wat]
- Watrous: Permutation invariance and unitarily invariant measures (lecture notes) B
- [AM]
- Anna Mele: Introduction to Haar measure tools in quantum information (review article) B

### Exact k-designs

- [DCE+]
- Dankert et al.: Exact and Approximate Unitary 2-Designs: Constructions and Applications M
- [DM]
- Di Matteo: A short introduction to unitary 2-designs B
- [Web]
- Webb: The Clifford group forms a unitary 3-design A
- [Zhu]
- Zhu: Multiqubit Clifford groups are unitary 3-designs A

### Decoupling in quantum information theory

- [Hay]
- Hayden: Decoupling: a building block for quantum information theory (tutorial) B
- [DBW+]
- Dupuis et al: One-shot decoupling M

### Random quantum channels and minimum output entropy

- [BH]
- Brandao, Horodecki: On Hastings' counterexamples to the minimum output entropy additivity conjecture A
- [FKM]
- Fukuda, King, Moser: Comments on Hastings' additivity counterexamples A

### Approximate designs

- [DCE+]
- see above ↑
- [BHH1]
- Brandao, Harrow, Horodecki: Local random quantum circuits are approximate polynomial-designs M A
- [BHH2]
- Brandao, Harrow, Horodecki: Efficient quantum pseudorandomness A
- [HM]
- Harrow, Mehraban: Approximate unitary t-designs by short random quantum circuits using nearest-neighbor and long-range gates A
- [HJ]
- Hunter-Jones: Unitary designs from statistical mechanics in random quantum circuits M

### High-energy physics and scrambling

- [HP]
- Hayden, Preskill: Black holes as mirrors: quantum information in random subsystems (research article) B
- [YK]
- Yoshida, Kitaev: Efficient decoding for the Hayden-Preskill protocol M
- [CHJ+]
- Cotler et al.: Chaos, complexity and random matrices M A
- [LLZ+]
- Liu et al.: Entanglement, quantum randomness, and complexity beyond scrambling M

### Miscellaneous

- [HLW]
- Hayden, Leung, Winter: Aspects of generic entanglement M A
- [ABF+]
- Aaronson et al.: Quantum pseudoentanglement M A
- [CMN]
- Collins et al: The Weingarten calculus A

## Quantum channel capacities

**Note:** This material is mainly concerned with quantum channel capacities in the finite-dimensional setting, which is the setting I focus on in my research.
There is a wealth of literature for quantum channel capacities in the continuous variable setting that I may add in the future. In the meantime, Section V in this review article on Gaussian quantum information and a slightly older review article on Gaussian quantum channels both give an excellent overview.

### Introductory articles, reviews, textbooks

- [Hol1]
- Holevo: Quantum channel capacities (review article) B
- [KW]
- Khatri, Wilde: Principles of Quantum Communication Theory: A Modern Approach (textbook) B M A
- [Smi1]
- Smith: Quantum Channel Capacities (review article) B
- [Wil]
- Wilde: Quantum Information Theory (textbook) B M A

### Coding theorems

- [BSS+]
- Bennett et al: Entanglement-Assisted Classical Capacity of Noisy Quantum Channels (research article) M
- [HMW+]
- Hayden et al.: A decoupling approach to the quantum capacity (research article) M
- [KW]
- see above ↑
- [SW]
- Schumacher, Westmoreland: Sending classical information via noisy quantum channels (research article) B M
- [Wil]
- see above ↑

### Additivity

- [BDS]
- Bennett, DiVincenzo, Smolin: Capacities of Quantum Erasure Channels (research article) B
- [BSS+]
- see above ↑
- [DS]
- Devetak, Shor: The capacity of a quantum channel for simultaneous transmission of classical and quantum information (research article) B M
- [Kin1]
- King: Additivity for a class of unital qubit channels (research article) B
- [Kin2]
- King: The capacity of the quantum depolarizing channel (research article) B M
- [LLS1]
- Leditzky, Leung, Smith: Quantum and private capacities of low-noise channels (research article) M
- [LLS+a]
- Leditzky et al.: The platypus of the quantum channel zoo (research article) M A
- [Sho1]
- Shor: Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels (research article) M
- [Sho2]
- Shor: Equivalence of Additivity Questions in Quantum Information Theory (research article) M
- [Smi2]
- Smith: The private classical capacity with a symmetric side channel and its application to quantum cryptography (research article) B
- [Wat]
- Watanabe: Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels (research article) M

### Non-additivity

- [BL]
- Bausch, Leditzky: Error Thresholds for Arbitrary Pauli Noise (research article) A
- [DWS]
- DiVincenzo, Shor, Smolin: Quantum Channel Capacity of Very Noisy Channels (research article) M A
- [FKM]
- Fukuda, King, Moser: Comments on Hastings' Additivity Counterexamples (research article) M A
- [LLS2]
- Leditzky, Leung, Smith: Dephrasure channel and superadditivity of coherent information (research article) M
- [LLS+b]
- Leditzky et al.: Generic nonadditivity of quantum capacity in simple channels (research article) M A
- [LLS+c]
- Leung et al.: Maximal Privacy Without Coherence (research article) M A
- [Sid]
- Siddhu: Entropic singularities give rise to quantum transmission (research article) M
- [SS]
- Smith, Smolin: Degenerate Quantum Codes for Pauli Channels (research article) A
- [SY]
- Smith, Yard: Quantum Communication With Zero-Capacity Channels (research article) M

## 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
- [FH]
- see above ↑

### Representation theory of Lie groups and Lie algebras

- [Ca1]
- Čap: Lie algebras and representation theory (lecture notes) B M
- [Ca2]
- Čap: 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
- [Ch]
- see above ↑
- [FH]
- see above ↑

### 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
- [Ch]
- see above ↑

### 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
- [Ch]
- see above ↑
- [Ha1]
- see above ↑
- [Wa]
- see above ↑