Foton istatistiklerinin kuantum rastgele sayı üreticileri ve foton algılama verimliliği üzerindeki etkileri

The effects of photon statistics on different quantum applications are explained in this thesis. There are mainly two sections: the first section focuses on the randomly bunched and coherently bunched photons' continuous detection. The second section focuses on the anti-bunched single-photon behavior and its single-photon detection. Random numbers are essential resources in cryptography, simulation technologies, and finance. The intrinsic behavior of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation (QRNG) is one of the most preferred quantum technologies with many alternative generation methods. Therefore, among the different technologies in quantum random number generation from the primal applications based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum base I have chosen to use the vacuum fluctuation method. In the first part of the thesis, the photon statistics of thermal and coherent light sources and their scatterings are compared. The sources with super-Poissonian distribution are shown to have better randomness than the Poisson distribution. The optimal sampling rate is obtained when the under-sampling is set as two times the lag point for the minimum autocorrelation of the scattered signal. The use of scattering mechanisms as an entropy source increased the speed and shortened the post-processing procedure significantly, opening the way for higher-speed QRNG generation technologies. In the second part of the thesis, I introduce an entanglement-based sensing protocol that achieves a signal to noise ratio (SNR) improvement over the optimal classical scheme in a highly lossy and noisy environment that completely breaks the initial entanglement property. Under high noise conditions, which might occur from the devices used in the experiment or the imperfections sources from the open system of the setup the heralding loss will be high. It is observed that the detectors also show measurement errors, under the effect of high noise conditions and from the limitations caused by their timing jitters. The biased behavior of the detectors in near saturation conditions is supported by the cross-correlogram measurements. Emphasis was placed on the unreliability in the detections when exceeding its limitations. In such conditions, it is not possible to use the quantum advantage of the system without making any adjustments. With the application presented in this section, the result of quantum sensing clearly demonstrates that a quantum resource can be utilized beneficially even when its initial non-classical character is lost, knowing all its shortcomings and limitations.