Given a biased coin with unknown success probability p, how can we simulate a coin with probability f(p)? Such randomness processing tasks are called Bernoulli factory problem. In 1992, Keane and O’Brien determined the exact set of simulable functions in the classical input classical output case. In 2015, Dale, Jennings and Ruldolph introduced the problem to the quantum world and consider the quantum input classical output case. They prove the simulable set in the quantum-to-classical case is strictly larger than the classical-to-classical case and thus prove a quantum advantage.
In this talk, we generalize Bernoulli factory problem to quantum input quantum output case. We give the full characterization of simulable quantum states and present an algorithm to transform them. We also compare the sets in the three cases and show that simulable sets in the quantum-to-quantum case and classical-to-classical case have no inclusion relationship with each other.
Dr. Jiang Jiaqing from Institute of Computing Technology, CAS