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dc.contributor.advisorDana Moshkovitz.en_US
dc.contributor.authorYuen, Henry, Ph. D. Massachusetts Institute of Technologyen_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2014-02-10T16:55:05Z
dc.date.available2014-02-10T16:55:05Z
dc.date.issued2013en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/84856
dc.descriptionThesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.en_US
dc.descriptionTitle as it appears in Degrees awarded booklet, September 2013: Upper and lower bounds for quantum randomness expansion. Cataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 62-64).en_US
dc.description.abstractA recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions: the prior existence of a short random seed and the ability to ensure that two black-box devices do not communicate (i.e. are non-signaling). We call protocols achieving such certified amplification of a short random seed randomness amplifiers. We introduce a simple framework in which we initiate the systematic study of the possibilities and limitations of randomness amplifiers. Our main results include a new, improved analysis of a robust randomness amplifier with exponential expansion, as well as the first upper bounds on the maximum expansion achievable by a broad class of randomness amplifiers. In particular, we show that non-adaptive randomness amplifiers that are robust to noise cannot achieve more than doubly exponential expansion. We show that a wide class of protocols based on the use of the CHSH game can only lead to (singly) exponential expansion if adversarial devices are allowed the full power of non-signaling strategies. Our upper bound results apply to all known non-adaptive randomness amplifier constructions to date. Finally, we demonstrate, for all positive integers k, a protocol involving 2k non-signaling black-box quantum devices that achieves an amount of expansion that is a tower of exponentials of height k. This hints at the intriguing possibility of infinite randomness expansion.en_US
dc.description.statementofresponsibilityby Henry Yuen.en_US
dc.format.extent64 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleQuantum randomness expansion : upper and lower boundsen_US
dc.title.alternativeUpper and lower bounds for quantum randomness expansionen_US
dc.typeThesisen_US
dc.description.degreeS.M.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.identifier.oclc868312145en_US


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