期刊
SIAM JOURNAL ON COMPUTING
卷 41, 期 4, 页码 915-940出版社
SIAM PUBLICATIONS
DOI: 10.1137/100813683
关键词
randomness extractors; quantum information; quantum cryptography; smooth min-entropy
资金
- Berkeley fellowship for graduate study
- Vienna Science and Technology Fund (WWTF) [ICT10-067]
- Swiss National Science Foundation [200021-119868, 200020-135048]
- Swiss National Science Foundation (National Centre of Competence in Research Quantum Science and Technology)
- European Research Council-ERC [258932]
- National Science Foundation [0844626]
- [NSF-CCF-1017403]
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.
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