Amplifying the randomness of weak sources correlated with devices

Hanna Wojewódka , Fernando G.S.L. Brandão , Andrzej Grudka , Karol Horodecki , Michał Horodecki , Paweł Horodecki , Marcin Pawłowski , Ravishankar Ramanathan , Maciej Stankiewicz


The problem of device-independent randomness amplification against no-signaling adversaries has so far been studied under the assumption that the weak source of randomness is uncorrelated with the (quantum) devices used in the amplification procedure. In this paper, we relax this assumption, and reconsider the original protocol of Colbeck and Renner using a Santha-Vazirani (SV) source. To do so, we introduce an SV-like condition for devices, namely that any string of SV source bits remains weakly random conditioned upon any other bit string from the same SV source and the outputs obtained when this further string is input into the devices. Assuming this condition, we show that a quantum device using a singlet state to violate the chained Bell inequalities leads to full randomness in the asymptotic scenario of a large number of settings, for a restricted set of SV sources (with 0≤ε<(2(1/12)−1)/(2(2(1/12)+1))≈0.0144 ). We also study a device-independent protocol that allows for correlations between the sequence of boxes used in the protocol and the SV source bits used to choose the particular box from whose output the randomness is obtained. Assuming the SV-like condition for devices, we show that the honest parties can achieve amplification of the weak source, for the parameter range 0≤ε<0.0132 , against a class of attacks given as a mixture of product box sequences, made of extremal no-signaling boxes, with additional symmetry conditions. Composable security proof against this class of attacks is provided.
Author Hanna Wojewódka
Hanna Wojewódka,,
, Fernando G.S.L. Brandão
Fernando G.S.L. Brandão,,
, Andrzej Grudka
Andrzej Grudka,,
, Karol Horodecki II
Karol Horodecki,,
- Institute of Informatics
, Michał Horodecki IFTiA
Michał Horodecki,,
- Institute of Theoretical Physics and Astrophysics
, Paweł Horodecki
Paweł Horodecki,,
, Marcin Pawłowski IFTiA
Marcin Pawłowski,,
- Institute of Theoretical Physics and Astrophysics
, Ravishankar Ramanathan IFTiA
Ravishankar Ramanathan,,
- Institute of Theoretical Physics and Astrophysics
, Maciej Stankiewicz IM
Maciej Stankiewicz,,
- Institute of Mathematics
Journal seriesIEEE Transactions on Information Theory, ISSN 0018-9448
Issue year2017
Publication size in sheets0.95
Keywords in Englishquantum cryptography, random number generation
Languageen angielski
Score (nominal)40
ScoreMinisterial score = 35.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.679 (2) - 2016=3.228 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.