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Randomness amplification against no-signaling adversaries using two devices

Ramanathan, Ravishankar and Brandão, Fernando G. S. L. and Horodecki, Karol and Horodecki, Michał and Horodecki, Paweł and Wojewódka, Hanna (2015) Randomness amplification against no-signaling adversaries using two devices. . (Submitted)

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Recently the first physically realistic protocol amplifying the randomness of Santha-Vazirani sources using a finite number of no-signaling devices and with a constant rate of noise has been proposed, however there still remained the open question 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 devices and in a situation where the violation of a Bell inequality implies only an upper bound for some outcome probability for some setting combination? Here, we solve this problem and present the first device-independent protocol for the task of randomness amplification of Santha-Vazirani sources using a device consisting of only two non-signaling components. We show that the protocol can amplify any such source that is not fully deterministic into a totally random source while tolerating a constant noise rate and prove the security of the protocol against general no-signaling adversaries. The minimum requirement for a device-independent Bell inequality based protocol for obtaining randomness against no-signaling attacks is that every no-signaling box that obtains the observed Bell violation has the conditional probability P(x|u) of at least a single input-output pair (u,x) bounded from above. We show how one can construct protocols for randomness amplification in this minimalistic scenario.

Item Type:Report or Paper (Discussion Paper)
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Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:The paper is supported by ERC AdG grant QOLAPS, EC grant RAQUEL and by Foundation for Polish Science TEAM project co-financed by the EU European Regional Development Fund. FB acknowledges support from EPSRC and Polish Ministry of Science and Higher Education Grant no. IdP2011 000361. Part of this work was done in National Quantum Information Center of Gdánsk. Part of this work was done when F. B., R. R., K. H. and M. H. attended the program “Mathematical Challenges in Quantum Information” at the Isaac Newton Institute for Mathematical Sciences in the University of Cambridge.
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
European CommissionUNSPECIFIED
Fundacja na rzecz Nauki PolskiejUNSPECIFIED
European Regional Development FundUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Ministerstwo Nauki i Szkolnictwa Wyższego (MNiSW)IdP2011 000361
Record Number:CaltechAUTHORS:20160608-092908091
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67760
Deposited By: Tony Diaz
Deposited On:08 Jun 2016 16:40
Last Modified:03 Oct 2019 10:08

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