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The discovery of the random purification channel has surprised many of us who work on quantum learning, as it is so natural a statement, so powerful a technique, and spent so long under our noses. In this talk, I will survey the developments it led to over this past year. I will also give a rough theory for why it took decades to find, including why it was found now.
I will survey the remarkable progress on explicit constructions of randomness extractors for structured sources, including independent sources, small-space sources, and related models. Much of this progress has been driven by the development of powerful new primitives, such as non-malleable extractors, correlation breakers, and leakage-resilient extractors. I will discuss these notions, the connections between them, and discuss interesting open directions.
