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Irreducible private states (Conference Presentation)

Wojewódka, Hanna and Brandão, Fernando G. S. L. and Grudka, Andrzej and Horodecki, Karol and Horodecki, Michal and Horodecki, Pawel and Ramanathan, Ravishankar and Stankiewicz, Maciej (2017) Irreducible private states (Conference Presentation). In: Quantum Information Science and Technology III. Proceedings of SPIE. No.10442. Society of Photo-Optical Instrumentation Engineers (SPIE) , Bellingham, WA, Art. No. 1044202. ISBN 9781510613485.

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The work concerns the problem of finding a protocol for randomness amplification secure against non-signaling adversary with polynomial number of devices, which allows for correlations between the device and the source of weak randomness. We focus on the epsilon-Santha-Vazirani sources, and provide two results in this direction. First we revisit the seminal protocol of R. Colbeck and R. Renner (CR protocol) of randomness amplification using Santha-Vazirani (SV) sources, and prove its security relaxing partially assumptions of independence between the devices and the source at a price of narrowed range of epsilon. The relaxation allows that the SV source can indicate as a final device from which randomness is taken choosen with uniform probability from the insecure devices. The proof of relaxation bases on the assumption which is a generalization of Santha-Vazirani condition - the SV condition for boxes: there does not exist a device such that given its inputs and outputs one can get to know the value of SV source by more than epsilon. Second, we prove security of the CR protocol allowing arbitrary correlations between SV source and device, up to the mentioned SV-box condition, and the assumption that the devices are not correlated with each other. We prove that if the final device chosen in the protocol was not secure, an independent tester could guess the value of SV source bits more than the SV-box condition allows. The strategy of a tester is to choose a random device out of the ones which do not satisfy condition of the Chain Bell inequality. The idea of the proof of the second result indicates that the CR protocol may be secure under attack which arbitrarily correlates SV with devices of arbitrary type, and is promising in studying this problem.

Item Type:Book Section
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Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2017 Society of Photo-Optical Instrumentation Engineers (SPIE).
Series Name:Proceedings of SPIE
Issue or Number:10442
Record Number:CaltechAUTHORS:20190827-110541191
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Official Citation:Hanna Wojewódka, Fernando G. S. L. Brandao, Andrzej Grudka, Karol Horodecki, Michal Horodecki, Pawel Horodecki, Ravishankar Ramanathan, and Maciej Stankiewicz "Irreducible private states (Conference Presentation)", Proc. SPIE 10442, Quantum Information Science and Technology III, 1044202 (19 October 2017);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98269
Deposited By: Tony Diaz
Deposited On:27 Aug 2019 18:35
Last Modified:16 Nov 2021 17:37

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