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Amplifying the randomness of weak sources correlated with devices

Wojewódka, H. and Brandão, F. and Grudka, A. and Horodecki, M. and Horodecki, K. and Horodecki, P. and Pawłowski, M. and Ramanathan, R. (2016) Amplifying the randomness of weak sources correlated with devices. . (Submitted)

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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 work, we relax this assumption, and reconsider the original protocol of Colbeck and Renner, Nature Physics 8, 450-454 (2012), on randomness amplification 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 against this attack for the parameter range 0 ≤ ε < 0.0132. We leave the case of a yet more general attack on the amplification protocol as an interesting open problem.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Brandão, F.0000-0003-3866-9378
Additional Information:We acknowledge useful discussions with Roger Colbeck, Renato Renner, Christopher Portmann, Gilles Pütz and Maciej Stankiewicz. This work is supported by the EU grant RAQUEL, and the ERC AdG QOLAPS.
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European Research Council (ERC)UNSPECIFIED
Record Number:CaltechAUTHORS:20160608-095147622
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67762
Deposited By: Tony Diaz
Deposited On:08 Jun 2016 16:59
Last Modified:03 Oct 2019 10:08

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