# MQC-MB: Multiphoton Quantum Communication Using Multiple-Beam Concept in Free Space Optical Channel
## 2 Related Works  
This section reviews several recent works on quantum cryptography protocols over the FSO channel. Several studies have been conducted to investigate the atmospheric and the single telescope design effects in transmitting quantum keys. [PERSON] and [PERSON] [18] revealed that the design of the telescope's transmitter and receiver play an important role to reduce the link loss. To control the geometric loss, the receiver aperture area needs to be increased so that the receiver telescope can collect more signals. This means that a realistic design of the receiving telescope can enhance the reception efficiency of the quantum signal. The utilization of the photon detector with high detection efficiency and short dead time also plays an important role to obtain a high key rate. The work in [19] proposed a subcarrier multiplexing multiple-input multiple-output (MIMO) QKD to improve the bit rate by implementing multiple parallel single-photon communication for different channels. Unfortunately, they did not measure the impacts of key rate generations. Due to the complications to define the exact atmospheric losses, several QKD experiments did not include detailed parameters while conducting those experiments [20]. They simply defined the overall atmospheric attenuation in decibel without presenting the calculations of geometrical losses. In [11; 12; 13], QKD based on single photon and its variants, decoy-state, and weak coherent pulse (WCP) were evaluated over the atmospheric turbulence channels. The most important criteria to evaluate the key rate in turbulence channels is the channel transmittance, which can be determined based on the probability distribution of the transmission coefficient (PDTC). However, all the works did not take into account the geometrical and atmospheric losses since the impact of losses contributed by the device itself was not thoroughly investigated. The implementation of multiple spatial modes of single-photon QKD in the parallel channel using an overlapping Gaussian beam array (OBGA) with optimized beam geometry was studied in [21]. With a number of parallel channels to transmit the light beam, this scheme can increase the SKR. However, this scheme suffers from crosstalk that happens in the parallel channel due to the effect of the free space turbulence. Later, the work in [22] studied a multi-channel by employing an array of back-propagation mode (BPM) QKD at the transmitter and receiver telescope to reduce the effects of atmospheric transmission and increase the SKR. The function of the transmitter and receiver arrays is to enable simultaneous communication between the sender and receiver. The parallel and multiplexing QKD system will significantly increase the bit rate. According to the researchers in [23], the transmission of BB84 using a parallel sideband channel can substantially improve the performance gain in terms of the correct bit rate. Their experiment's results showed that the QKD with polarization coding in multiple subcarriers achieved a better value of QBER compared to without polarization coding. Although the usage of the multiple-beam technique in multiphoton quantum cryptography has not been discussed yet, it is worthy of being implemented in the multiphoton protocol to improve the transmission efficiency. To the best of our knowledge, the implementation of multiple-beam FSO to transmit multiphoton is proposed here for the first time. It is found in the literature that the ordinary single-beam FSO system has the limitations of limited received power, distance, and scalability. Therefore, this paper presents the performance evaluation of multiphoton quantum cryptography over the ground to ground FSO by including the important parameters to simulate the channel loss. In this paper, the impacts of atmospheric turbulence are included due to its effect of causing fluctuation in the transmittance, which significantly affects the QBER and SKR [13].