Tilted Hardy paradoxes for device-independent randomness extraction

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.

16+19 pages, 4+3 figures. Accepted in Quantum

References in corpus (6)

• Device-independent security of quantum cryptography against collective attacks
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Self testing quantum apparatus
• Large violations in Kochen Specker contextuality and their applications
• No-signaling-proof randomness extraction from public weak sources

Cited by in corpus (5)

• Test of the physical significance of Bell nonlocality
• Generalised Kochen-Specker Theorem for Finite Non-Deterministic Outcome Assignments
• Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario
• Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations
• (Almost-)Quantum Bell Inequalities and Device-Independent Applications