# Recent Progress in Multiplexed Single-Photon Sources
## 5 Theoretical Results and Experiments
### Application of Single-Photon Sources  
Single photons can be used as qubits encoding the quantum information in any of its degrees of freedom, for example, path, polarization, or time bin. They are largely free of noise or decoherence and can be easily manipulated. In the fields of quantum information processing and photonic quantum technology, there are several experiments and numerous applications where SPSs are key elements [1; 2; 3; 4; 5; 6].  
One group of them are quantum key distribution (QKD) protocols that ensure the secure generation of keys between two points of a communication network [136; 137; 138; 139; 140; 141]. A widely adapted protocol is BB84, which is based on the transmission and measurement of individual photons [142]. QKD systems have already been realized and used in practice [143; 144; 145; 146; 147]. Note that these systems generally apply laser systems, which generate weak coherent states instead of single photons. Nevertheless, the application of real SPSs would increase the security level and their efficiency. The performance of multiplexed SPSs in a practical QKD implementation has been analyzed in Ref. [148] by evaluating the achievable key rates.  
Another type of quantum communication is quantum teleportation that aims at transferring a quantum state between distant nodes of a network [149; 150]. Quantum teleportation of photonic qubits has been successfully performed in several experiments [151; 152; 153; 154; 155; 156].  
SPSs are fundamental building blocks in linear optical quantum computing [1; 4; 5; 157] Multiplexed SPSs are good candidates to meet all the criteria needed for the practical realization of this type of computing. These requirements, that is, high fidelity (\(g^{(2)}<0.07\)) and single-photon probability (\(P_{1}>0.9\)), were determined in Ref. [158]. Another type of quantum computing is one-way quantum computing, which is based on the generation of a highly entangled cluster state [1; 3; 4; 5; 159; 160; 161; 162]. In this approach, the computation is performed by a processing circuit consisting only of single-qubit measurements and feedforward operations.  
Though cluster states are generally prepared by using entangled photon pair sources [163; 164; 165; 166; 167; 168], SPSs can be also used for their efficient preparation [169; 170; 171; 172; 173].  
Boson sampling is a non-universal photonic quantum computing protocol where quantum computation supremacy over classical computers can be demonstrated [174]. Boson sampling has been realized successfully in several experiments [175; 176; 177; 130]. Multiple indistinguishable single-photon inputs of boson sampling scheme can be ensured by demultiplexing of the stream of photons of the SPS [179].  
Quantum memories in which the state of photonic qubits generated by SPSs can be stored are important elements of several optical quantum protocols [180; 181; 182; 183; 184; 185; 186; 187; 188]. One type of optical quantum memories is based on storage loops or cavities used in temporally multiplexed SPSs [180; 184; 185; 187; 188; 189].  
In addition to these applications in quantum information processing, efficient SPSs producing single-photon states are also assumed in several quantum optical schemes for generating quantum states of light [190; 191; 192; 193; 194; 195; 196; 197; 198] and in experiments investigating the quantum nature of light [199; 200].  
Finally, we note that in the experiments and in the applications realized in practice in the reviewed areas of applications, quantum dot-based or heralded SPSs have been used. The practical application of multiplexed SPSs in these areas is hindered by the fact that such sources have been realized experimentally only in laboratories; presently, no compact version of them is available.