Extracting classical randomness in a quantum world

Extractors are functions that transform a weakly random value X into an almost perfectly uniform value Z. Traditionally, extractors have been studied in a context where the side information, relative to which the distributions of X and Z are defined, is purely classical. Only recently, the notion of extractors has been generalized to scenarios where side information might be represented by the state of a quantum-mechanical system (while X and Z are still classical). This generalization is crucial for numerous applications, e.g., in cryptography, where an adversary might hold quantum-mechanical side information. In this article, we review this generalized notion of extractors as well as a construction of extractors based on two-universal hashing.