**Quantum error correction and multipartite entanglement** - Andrew Scott

Quantum error correction negates a quantum state\'s natural susceptibility to decohere, and thus provides the long-time coherence necessary to sustain quantum computation. Beginning with a concise introduction to quantum error-correcting codes, we will investigate the integrity of a code when pushed beyond its intended capacity, presenting formulae for the probability of failure when the errors affect more qudits than that specified by the code\'s minimum distance. We then expose a connection between multipartite entanglement and quantum error-correcting codes by deriving a formula relating the weight distribution of the code to the average entanglement of encoded states.