Infinite randomness expansion with a constant number of devices

Abstract

We present a device-independent randomness expansion protocol, involving only a constant number of non-signaling quantum devices, that achieves infinite expansion: starting with m bits of uniform private randomness, the protocol can produce an unbounded amount of certified randomness that is exp(--Ω(m1/3))-close to uniform and secure against a quantum adversary. The only parameters which depend on the size of the input are the soundness of the protocol and the security of the output (both are inverse exponential in m). This settles a long-standing open problem in the area of randomness expansion and device-independence.