# Recent Progress in Multiplexed Single-Photon Sources
## 6 Discussion  
In this review, we have summarized the progress in multiplexed single-photon sources. Special attention has been paid to the detailed presentation of the recent theoretical results that can help the experimental realization of high-performance single-photon sources. The theoretical results show and successful experiments demonstrate that multiplexed single-photon sources can produce highly indistinguishable single photons in near-perfect spatio-temporal modes with known polarization and with a high single-photon probability in a pseudo-deterministic way. Multiplexed sources can produce single photon signals with higher single-photon probabilities accompanied by lower multi-photon contribution compared to a heralded source alone. The performance of a multiplexed single-photon source is determined by the losses of the system such as the losses of the switching elements and the delay lines and the efficiencies of the detectors for heralding. There has been remarkable progress in the field of producing low-loss optical elements and devices that will probably proceed. For example, photon-number-resolving detectors with high detector efficiencies and low dark counts are now available for experiments. Obviously, a system characterized by lower losses can produce higher single-photon probabilities. According to the theoretical analyses, by using optical elements characterized by the same parameters in a multiplexed single-photon source, the application of different multiplexing types and schemes in a single-photon source can result in different performances. The actual set of loss parameters determines which of the multiplexing schemes will provide the highest performance single-photon source. The most important result of the theoretical analysis of multiplexed single-photon sources is that they can be optimized, that is, it is possible to determine optimal values for the system size and the number of photon pairs generated in the multiplexed units for which the output single-photon probability is maximal. The optimal system size is generally lower when detectors with higher efficiencies are used in the multiplexed units. The single-photon probability can be further increased by the unit-wise optimization of the number of generated photon pairs. The multiphoton contribution at the output of a multiplexed single-photon source can be decreased by decreasing the input mean photon number in the multiplexed units. This leads to a decrease in the single-photon probability that can be minimized by determining a novel optimal system size by reoptimizing the system. The theoretical analyses also showed that high single-photon probabilities can be achieved even for suboptimal system sizes with optimized input mean photon numbers. Successful multiplexed single-photon source experiments have demonstrated the usefulness of multiplexing, but most of them have not produced single-photon probabilities high enough for most of the applications, except for the two experimentally realized temporally multiplexed single-photon sources reported in Refs. [62; 70]. Several successful multiplexed source experiments have already applied integrated optical elements. Realizing fully integrated multiplexed sources is a promising future research direction as most of the applications require robust and compact single-photon sources. Advance in the development of efficient low-loss integrated optical elements is needed for proceeding in this area. Application of the summarized theoretical results in future experiments can further improve the performance of multiplexed single-photon sources. All the reviewed theoretical and experimental results anticipate that, in the near future, multiplexed single-photon sources can meet all the criteria posed on single-photon sources by the various applications. **Author Contributions:** Conceptualization, P.A. ; writing--original draft preparation, M.M. ; writing--review and editing, P.A. and M.M. All authors have read and agreed to the published version of the manuscript.