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Randomness extraction involves the processing of purely classical informationand is therefore usually studied in the framework of classical probabilitytheory. However, such a classical treatment is generally too restrictive forapplications, where side information about the values taken by classical randomvariables may be represented by the state of a quantum system. This isparticularly relevant in the context of cryptography, where an adversary maymake use of quantum devices. Here, we show that the well known constructionparadigm for extractors proposed by Trevisan is sound in the presence ofquantum side information.  We exploit the modularity of this paradigm to give several concrete extractorconstructions, which, e.g, extract all the conditional (smooth) min-entropy ofthe source using a seed of length poly-logarithmic in the input, or onlyrequire the seed to be weakly random.

Trevisan's extractor in the presence of quantum side information