Infinite Randomness Expansion and Amplification with a Constant Number of Devices

Understand

We present a device-independent randomness expansion protocol, involving only a constant number of non-signaling quantum devices, that achieves \emph{infinite expansion}: starting with $m$ bits of uniform private randomness, the protocol can produce an unbounded amount of certified randomness that is $\exp(-\Omega(m^{1/3}))$-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.
• The analysis of our protocols involves overcoming fundamental challenges in the study of \emph{adaptive} device-independent protocols.