# Recent Progress in Multiplexed Single-Photon Sources
## 1 Introduction  
Single-photon sources are fundamental elements in various experiments and numerous applications in the fields of quantum information processing and photonic quantum technology [1; 2; 3; 4; 5; 6]. An ideal single-photon source can produce highly indistinguishable photons with known polarization in near-perfect spatial modes in a deterministic way. Promising candidates for realizing such a perfect source are multiplexed single-photon sources [7; 8; 9; 10; 11]. The building elements of such sources are heralded single-photon sources [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36] that rely on some nonlinear optical processes, such as spontaneous parametric down-conversion or four-wave mixing, in which photon pairs are generated. The detection of one member of a pair announces the presence of its twin photon that yields the output of the heralded source. Though heralded single-photon sources are capable of generating indistinguishable photons in near-perfect spatial modes, the probabilistic nature of the underlying processes poses a limitation on the probability of obtaining exactly one photon at the output in a given period of operation, and there is always a finite probability of obtaining more than one photon from the source. Unfortunately, the reduction of this multiphoton contribution by reducing the average number of the photon pairs generated in the nonlinear processes also leads to a reduction in the single-photon probability and increases the probability of obtaining no photons at the output. Multiplexing several low-probability heralded single-photon sources provides a solution to overcome this problem by increasing the probability of successful heralding.  
Since the first proposals of multiplexed single-photon sources approximately two decades ago, numerous multiplexing schemes have been proposed and analyzed theoretically [37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57]. Also, several experimental research projects have been performed that proved the feasibility and the advantages of such sources [58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72].  
In this paper, we give an overview of the recent progress in multiplexed single-photon sources. As the basic building blocks of such sources are heralded single-photon sources, in Section 2, we summarize their basic characteristics. Heralding involves photon detection; therefore, this section contains an overview of photon-number-resolving detectors, which improve the performance of these sources. In Section 3, we expound on the operation principles of multiplexed single-photon sources, and we summarize the various multiplexingschemes proposed for realizing different types of multiplexing such as spatial, temporal, and spectral multiplexing. Next, in Section 4, we present the general theory capable of treating single-photon sources based on any type of multiplexer. Then, in Section 5, we present those theoretical results that are relevant from the point of future multiplexed single-photon source experiments and the practical realization of such sources. At the end of this section, we also give a summary of the successful experiments in which single-photon sources based on some kind of multiplexing were realized. Finally, we summarize the main points of the review and discuss the prospects of multiplexed single-photon sources.