Optimal Randomness Amplification schemes from Hardy paradoxes

Abstract

Randomness amplification, the task of obtaining secure random bits from weak sources of randomness, is a fundamental cryptographic task. Deviceindependent protocols for this task secure against no-signaling adversaries have so far relied on specific proofs of non-locality termed pseudo-telepathy games, and have remained out of reach of experimental implementation. In this talk, we will relate the problem of finding experimentally friendly randomness amplification schemes to the vast field of Hardy paradoxes and, as a consequence, present a device-independent randomness amplification protocol secure against no-signaling adversaries in the simplest experimentally feasible Bell scenario of two parties with two binary inputs. Furthermore, we will show that just as proofs of the Kochen-Specker theorem give rise to pseudo-telepathy games, substructures within these proofs termed 01-gadgets give rise to Hardy paradoxes and we will use them to construct Hardy paradoxes with the non-zero probability taking any value in (0,l]. Finally, we will see how to design optimal randomness amplification schemes based on Hardy paradoxes from arbitrary entangled twoqubit states.