Year: 2013
Type: preprint
Abstract: 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. Finally, 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.
Source: arXiv (Cornell University)
Authors: Coudron, Matthew, Vidick, Thomas, Yuen, Henry
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G2329501910, Graduate Research Fellowship Program, G3882347383, AF: Small: Sliding Scale Problems in Probabilistic Checking of Proofs, IGERT: Interdisciplinary Quantum Information Science and Engineering: a Graduate Research and Training Program, CAREER: Efficient Computation in the Physical World, G7712274940, G7827523863, G8729383044
OpenAlex ID: W2950859800