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Amplifying the Randomness of Weak Sources Correlated With Devices

Abstrakt

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.

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Autorzy (9)

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
IEEE TRANSACTIONS ON INFORMATION THEORY nr 63, strony 7592 - 7610,
ISSN: 0018-9448
Język:
angielski
Rok wydania:
2017
Opis bibliograficzny:
Horodecki P., Wojewódka H., Brandao F., Grudka A., Horodecki K., Horodecki M., Ramanathan R., Stankiewicz, M., Pawłowski, M.: Amplifying the Randomness of Weak Sources Correlated With Devices// IEEE TRANSACTIONS ON INFORMATION THEORY. -Vol. 63, nr. 11 (2017), s.7592-7610
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1109/tit.2017.2738010
Weryfikacja:
Politechnika Gdańska

wyświetlono 27 razy

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