General quantum Bernoulli factory: framework analysis and experiments

Abstract

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

Polarization-encoded photonic quantum-to-quantum Bernoulli factory based on a quantum dot source

“…Second, the implementation should feature modularity, i.e., the ability of chaining together several QQBF or integrating them as a processing step in a more general algorithm. Most previous experimental demonstrations of QQBF (14,15) were essentially unable to fulfill these two requirements.…”

“…In literature, different experiments have attempted to realize a QQBF using photonic-based platforms, but they fail in proposing a general approach in which different operations can be concatenated without any knowledge about the input quantum state (14,15). We note that recent advances in photonic technologies (26) have enabled the realization of system setups comprising several optical spatial modes and components, enabled by the properties and the encoding schemes of integrated platforms (27)(28)(29)(30).…”

“…F Exp sum = 0.973 ± 0.025, F Exp amean = 0.978 ± 0.022. (15) scheme, the corresponding input pairs {|z 1 〉, |z 2 〉} appear to be more sensitive to both an imperfect compensation of the polarizationdependent phase shift introduced by the first BS and imperfect indistinguishability. When accounting for the latter effect, the corrected visibility for such states lies in all cases in the interval (0.75,0.9), i.e., the tail of the overall distribution reported in Fig.…”

“…Given the broad applicability of such a problem, in recent years, quantum counterparts to the BF problem were theoretically introduced (10)(11)(12) and experimentally implemented (13)(14)(15)(16). In the quantum-to-classical version of a BF (10,11), the input classical coin is replaced by a quantum coin represented by a two-dimensional state |p⟩.…”