### Group representations and quantum information theory

Harrow, A *(Massachusetts Institute of Technology)*

Tuesday 15 October 2013, 10:00-11:00

Seminar Room 1, Newton Institute

#### Abstract

The method of types---classifying strings according to letter frequencies---is a fundamental tool of classical information theory. I will discuss a natural quantum generalisation, known as the Schur basis, in which quantum states are decomposed into irreps of the unitary and symmetric groups. First, I'll explain the analogy to the classical method of types and will review past work that applies the Schur basis to quantum information theory. Then I'll discuss applications to spectrum estimation, channel coding problems and mention some open problems.

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