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# Math 401, Paper 1: Concentration of measure effects in quantum information (Patrick Hayden)
[PDF](https://www.ams.org/books/psapm/068/2762144)
## Quantum codes
### Preliminaries
#### Daniel Gottesman's mathematics of quantum error correction
##### Quantum channels
Encoding channel and decoding channel
#### Quantum capacity for a quantum channel
#### Lloyd-Shor-Devetak theorem
### Surprise in high-dimensional quantum systems
#### Levy's lemma
### Random states and random subspaces
#### ebits and qbits
### Superdense coding of quantum states
### Consequences for mixed state entanglement measures
#### Quantum mutual information
### Multipartite entanglement