Trevisan's Extractor in the Presence of Quantum Side Information
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 cla...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/1721.1/77888 |
| _version_ | 1826194418354356224 |
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| author | De, Anindya Portmann, Christopher Vidick, Thomas Renner, Renato |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory De, Anindya Portmann, Christopher Vidick, Thomas Renner, Renato |
| author_sort | De, Anindya |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:55:48Z |
| format | Article |
| id | mit-1721.1/77888 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:55:48Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/778882022-09-30T17:46:01Z Trevisan's Extractor in the Presence of Quantum Side Information De, Anindya Portmann, Christopher Vidick, Thomas Renner, Renato Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Vidick, Thomas 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. National Science Foundation (U.S.) (Grant 0844626.) 2013-03-13T18:34:49Z 2013-03-13T18:34:49Z 2012-08 2010-11 Article http://purl.org/eprint/type/JournalArticle 0097-5397 1095-7111 http://hdl.handle.net/1721.1/77888 De, Anindya et al. “Trevisan’s Extractor in the Presence of Quantum Side Information.” SIAM Journal on Computing 41.4 (2012): 915–940. © 2012, Society for Industrial and Applied Mathematics en_US http://dx.doi.org/10.1137/100813683 SIAM Journal on Computing Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | De, Anindya Portmann, Christopher Vidick, Thomas Renner, Renato Trevisan's Extractor in the Presence of Quantum Side Information |
| title | Trevisan's Extractor in the Presence of Quantum Side Information |
| title_full | Trevisan's Extractor in the Presence of Quantum Side Information |
| title_fullStr | Trevisan's Extractor in the Presence of Quantum Side Information |
| title_full_unstemmed | Trevisan's Extractor in the Presence of Quantum Side Information |
| title_short | Trevisan's Extractor in the Presence of Quantum Side Information |
| title_sort | trevisan s extractor in the presence of quantum side information |
| url | http://hdl.handle.net/1721.1/77888 |
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