Randomness Amplification under Minimal Fundamental Assumptions on the Devices

Ravishankar Ramanathan; Fernando Brandão; Karol Horodecki; Michał Horodecki; Paweł Horodecki; Hanna Wojewódka

doi:10.1103/physrevlett.117.230501

Randomness Amplification under Minimal Fundamental Assumptions on the Devices

Abstract

Recently, the physically realistic protocol amplifying the randomness of Santha-Vazirani sources producing cryptographically secure random bits was proposed; however, for reasons of practical relevance, the crucial question remained open regarding whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two no-signaling components and in a situation where the violation of a Bell inequality only guarantees that some outcomes of the device for specific inputs exhibit randomness? Here, we solve this question and present a device-independent protocol for randomness amplification of Santha-Vazirani sources using a device consisting of two nonsignaling components. We show that the protocol can amplify any such source that is not fully deterministic into a fully random source while tolerating a constant noise rate and prove the composable security of the protocol against general no-signaling adversaries. Our main innovation is the proof that even the partial randomness certified by the two-party Bell test [a single input-output pair (u∗, x∗) for which the conditional probability P(x∗|u∗) is bounded away from 1 for all no-signaling strategies that optimally violate the Bell inequality] can be used for amplification. We introduce the methodology of a partial tomographic procedure on the empirical statistics obtained in the Bell test that ensures that the outputs constitute a linear min-entropy source of randomness. As a technical novelty that may be of independent interest, we prove that the Santha-Vazirani source satisfies an exponential concentration property given by a recently discovered generalized Chernoff bound.

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Authors (6)

Ravishankar Ramanathan
- Univ Gdanski Natl Quantum Informat Ctr
Fernando Brandão
- Microsoft Research, Redmond, USA Quantum Architectures and Computation Group
Karol Horodecki
- Univ Gdanski Natl Quantum Informat Ctr
Michał Horodecki
- Univ Gdanski Natl Quantum Informat Ctr
Paweł Horodecki prof. dr hab.
Hanna Wojewódka
- Univ Slaski Institute of Mathematics

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DOI:: Digital Object Identifier (open in new tab) 10.1103/PhysRevLett.117.230501
License: Copyright (2016 American Physical Society)

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: PHYSICAL REVIEW LETTERS no. 117, edition 23, pages 1 - 5,
ISSN: 0031-9007
Language:: English
Publication year:: 2016
Bibliographic description:: Ramanathan R., Brandão F., Horodecki K., Horodecki M., Horodecki P., Wojewódka H.: Randomness Amplification under Minimal Fundamental Assumptions on the Devices// PHYSICAL REVIEW LETTERS. -Vol. 117, iss. 23 (2016), s.1-5
DOI:: Digital Object Identifier (open in new tab) 10.1103/physrevlett.117.230501
Verified by:: Gdańsk University of Technology