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 using quantum coherence and single-qubit measurements and the other one using 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 fivefold reduction. These concepts may provide a means for quantum-enhanced performance in the simulation of stochastic processes and sampling tasks.