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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
+