Quantum randomness expansion : upper and lower bounds
Author(s)Yuen, Henry, Ph. D. Massachusetts Institute of Technology
Upper and lower bounds for quantum randomness expansion
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
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A 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.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Title as it appears in Degrees awarded booklet, September 2013: Upper and lower bounds for quantum randomness expansion. Cataloged from PDF version of thesis.Includes bibliographical references (pages 62-64).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.