Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries

• URL: http://arxiv.org/abs/2409.20082v1
• Date: Mon, 30 Sep 2024 08:31:46 GMT
• Title: Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries
• Authors: Jaskaran Singh, Cameron Foreman, Kishor Bharti, Adán Cabello,
• Abstract summary: We show that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our schemeally produces secure random numbers which are $mathcalO(mstepsilon)$-close to uniformly distributed and private.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In quantum cryptography, secure randomness expansion involves using a short private string of random bits to generate a longer one, even in the presence of an adversary who may have access to quantum resources. In this work, we demonstrate that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against computationally unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our scheme asymptotically produces secure random numbers which are $\mathcal{O}(m\sqrt{\epsilon})$-close to uniformly distributed and private, where $\epsilon$ is the robustness parameter of the self-test and $m$ is the length of the generated random bit string. Our protocol is semi-device-independent in the sense that it inherits any assumptions necessary for the underlying self-test.

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