  There has been a concerted effort to identify problems computable with
quantum technology which are intractable with classical technology or require
far fewer resources to compute. Recently, randomness processing in a Bernoulli
factory has been identified as one such task. Here, we report two quantum
photonic implementations of a Bernoulli factory, one utilising quantum
coherence and single-qubit measurements and the other which uses quantum
coherence and entangling measurements of two qubits. We show that the former
consumes three orders of magnitude fewer resources than the best known
classical method, while entanglement offers a further five-fold reduction.
These concepts may provide a means for quantum enhanced-performance in the
simulation of stochastic processes and sampling tasks.
