# 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