Tilted Hardy paradoxes for device-independent randomness extraction
- URL: http://arxiv.org/abs/2205.02751v4
- Date: Tue, 12 Sep 2023 04:45:29 GMT
- Title: Tilted Hardy paradoxes for device-independent randomness extraction
- Authors: Shuai Zhao, Ravishankar Ramanathan, Yuan Liu, and Pawe{\l} Horodecki
- Abstract summary: We introduce a family of tilted Hardy paradoxes that allow to self-test general pure two-qubit entangled states.
We also introduce a family of Hardy tests for maximally entangled states of local dimension $4, 8$ as the potential candidates for DI randomness extraction.
- Score: 5.802194744651422
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- 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.
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