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The unremitting pursuit for quantum advantages gives rise to the discovery ofa quantum-enhanced randomness processing named quantum Bernoulli factory (QBF).This quantum enhanced process can show its priority over the correspondingclassical process through readily available experimental resources, thus in thenear term it may be capable of accelerating the applications of classicalBernoulli factories, such as the widely used sampling algorithms. In this work,we provide the framework analysis of the QBF. We thoroughly analyze the quantumstate evolution in this process, discovering the field structure of theconstructible quantum states. Our framework analysis shows that naturally, theprevious works can be described as specific instances of this framework. Then,as a proof of principle, we experimentally demonstrate this framework via anentangled two-photon source along with a reconfigurable photonic logic, andshow the advantages of the QBF over the classical model through a classicallyinfeasible instance. These results may stimulate the discovery of advantages ofthe quantum randomness processing in a wider range of tasks, as well as itspotential applications.

General Quantum Bernoulli Factory: Framework Analysis and Experiments