Trevisan's extractor in the presence of quantum side information

Anindya De*, Christopher Portmann, Thomas Vidick, Renato Renner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Scopus citations


Randomness extraction involves the processing of purely classical information and is therefore usually studied with in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for applications where side information about the values taken by classical random variables may be represented by the state of a quantum system. This is particularly relevant in the context of cryptography, where an adversary may make use of quantum devices. Here, we show that the well-known construction paradigm for extractors proposed by Trevisan is sound in the presence of quantum side information. We exploit the modularity of this paradigm to give several concrete extractor constructions, which, e.g., extract all the conditional (smooth) min-entropy of the source using a seed of length polylogarithmic in the input, or only require the seed to be weakly random.

Original languageEnglish (US)
Pages (from-to)915-940
Number of pages26
JournalSIAM Journal on Computing
Issue number4
StatePublished - 2012


  • Quantum cryptography
  • Quantum information
  • Randomness extractors
  • Smooth min-entropy

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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