1Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
2International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
3Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
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Abstract
The device-independent paradigm has had spectacular successes in randomness generation, key distribution and self-testing, however most of these results have been obtained under the assumption that parties hold trusted and private random seeds. In efforts to relax the assumption of measurement independence, Hardy’s non-locality tests have been proposed as ideal candidates. In this paper, we introduce a family of tilted Hardy paradoxes that allow to self-test general pure two-qubit entangled states, as well as certify up to $1$ bit of local randomness. We then use these tilted Hardy tests to obtain an improvement in the generation rate in the state-of-the-art randomness amplification protocols for Santha-Vazirani (SV) sources with arbitrarily limited measurement independence. Our result shows that device-independent randomness amplification is possible for arbitrarily biased SV sources and from almost separable states. Finally, we introduce a family of Hardy tests for maximally entangled states of local dimension $4, 8$ as the potential candidates for DI randomness extraction to certify up to the maximum possible $2 log d$ bits of global randomness.
Featured image: Lower bound on the maximal achievable entropy of $I_{alpha}^{MDL}$ ($alpha=frac{1}{2},alpha=frac{4}{5},alpha=1$) versus the lower bound $l$ of a weak SV-source.
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Cited by
[1] Ravishankar Ramanathan, “Finite Device-Independent Extraction of a Block Min-Entropy Source against Quantum Adversaries”, arXiv:2304.09643, (2023).
[2] Abhishek Sadhu and Siddhartha Das, “Testing of quantum nonlocal correlations under constrained free will and imperfect detectors”, Physical Review A 107 1, 012212 (2023).
[3] Yuan Liu, Ho Yiu Chung, and Ravishankar Ramanathan, “Investigations of the boundary of quantum correlations and device-independent applications”, arXiv:2309.06304, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2023-09-15 11:06:11). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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