Infinite Randomness Expansion with a Constant Number of Devices
Randomness expansion protocols allow a classical user to certify that untrusted quantum devices output genuinely random bits, while starting with an amount of seed randomness that's much smaller than the output. A natural question is: what is the maximum amount of certifiable output randomness, given some starting amount of seed randomness? In this talk, I'll describe certain cases in which this maximum amount is bounded, and other cases in which there is no upper bound. In particular, I'll describe a protocol where, starting with a constant amount of seed randomness, a classical user can certify an arbitrarily long amount of output randomness. Its analysis involves interesting questions about securely composing quantum protocols.
Based on joint works with Matthew Coudron and Thomas Vidick.