Simulating single photons with realistic photon sources

Quantum information processing provides remarkable advantages over its classical counterpart. Quantum optical systems have been proved to be sufficient for realizing general quantum tasks, which, however, often rely on single-photon sources. In practice, imperfect single-photon sources, such as a weak-coherent-state source, are used instead, which will inevitably limit the power in demonstrating quantum effects. For instance, with imperfect photon sources, the key rate of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol will be very low, which fortunately can be resolved by utilizing the decoy-state method. As a generalization, we investigate an efficient way to simulate single photons with imperfect ones to an arbitrary desired accuracy when the number of photonic inputs is small. Based on this simulator, we can thus replace the tasks that involve only a few single-photon inputs with the ones that make use of only imperfect photon sources. In addition, our method also provides a quantum simulator to quantum computation based on quantum optics. In the main context, we take a phase-randomized coherent state as an example for analysis. A general photon source applies similarly and may provide some further advantages for certain tasks.