# MQC-MB: Multiphoton Quantum Communication Using Multiple-Beam Concept in Free Space Optical Channel
## 6 Numerical Results and Performance Analysis
In this research, the four beam at the same wavelength is used as the improvement of the single beam since the highest number of the beam will increase the sensitivity of the FSO receiver [32]. From now onwards, the standard beam is represented as a single beam while the four beam is represented as a multiple beam. Figure 7 illustrates the relationship between the link range and QBER for the two sets of beams. QBER in this work can be defined as the probability of bits in error by Bob's detection. As shown in Figure 8, the QBER increases to reach the maximum distance for \(N_{max}=12\). The QBER of the multiple beam shows the lowest value due to less photon losses during the transmission. Since the multiple beam produces a lower total loss compared to the single beam, the ability of the photon to be delivered to the receiver is increased. Thus, the multiple beam will generate lower QBER as the photons travel over the low loss channel. It can be concluded that the geometrical attenuation effect can reduce QBER when the link range increased compared to the single beam. Figure 6: Received power for single and multiple transmitter/receiver. Figure 8 illustrates the secret key rate and maximum distances that can be achieved by the single beam and multiple beam to transfer the secret keys between the sender and receiver for \(N_{max}=12\). In this work, the probability of obtaining a bit of a secret key per transmitted quantum signal pulse can be described by SKR. It is found that the SKR of the multiple beam is higher compared to the single beam due to the increased number of beams that will escalate the sensitivity of the receiver to detect the photons. SKR is also affected by the amount of QBER as discussed in Figure 8. The probability of getting a secret key bit per signal is higher when using multiple beams. The reason for this situation is the redundant laser paths will increase the transmission and detection of photons. Accordingly, the implementation of multiple beams will significantly increase the link distance by 1 km. A longer distance of FSO is achieved using the multiple beam due to the total loss of the transmitting laser beams in the communication path being reduced. A comparative analysis of the secret key rates for three sets of maximum photon number \(N\) with different sets of the beam is shown in Figure 9. The bar chart indicates improved secret key rates with the multiple beam, with an average of 35%. It can be observed from the results that the multiple beam contributes in improving the communication distance and also yields better secret key rates as compared to the single beam. The improvements are mainly due to the reduced impact of noise affected by the geometrical loss error. Therefore,  
Figure 8: Comparison of Secret Key Rate for \(N_{max}=12\). Figure 7: Comparison of QBER for \(N_{max}=12\). the proposed multiple beam is suitable to be implemented with various photon numbers to achieve an optimum key generation rate. In the second part of the evaluation, a significant improvement of SKR can be gained by implementing the proposed multiple beam in the presence of strong, moderate, and weak atmospheric turbulence effects as presented in Figure 10 and Table 2. As mentioned in Section 3, the SKR is computed by integrating \(K(\eta)\) over all possible \(\eta\) from zero to one with the PDTC function, which is a log-normal distribution. Here, we use the value of mean \(\eta_{0}=0.3\) and the variance \(\sigma=0.3,\ 0.6\) and \(0.9\)[13] to plot the graph. It can be seen that the multiple beam shows an improvement by producing higher SKR and is more tolerant to loss by 26 dB versus 20 dB for the single beam, with a 6-dB increase in intolerant loss for all variances. These outcomes indicate that MQC-MB outperforms the single-beam approach in terms of the reduction of geometric losses in all turbulence effects. While, in the single beam, the results prove that the geometrical losses are significantly large due to utilizing single-photon transmission for sending the information or key.