## 3 Research Methodology
### Experimental Design  
From the comprehensive listing of decoy state configurations captured in Table 4, and detailed understanding of the decoy state protocol, five experimental factors are identified as shown in Table 5. First, operational distances of 20 and 50 km are selected to represent common metropolitan network lengths and long-haul backbone links. For those not familiar with quantum communication, losses of \(\sim\)0.2 dB per km in single mode fiber significantly limit propagation distances where 20 km equates to 4 dB loss (or 40% efficiency) and 50 km equates to 10 dB loss (or 10% efficiency) [1]. Next, signal and decoy MPNs representative of normal and high configurations are chosen for examination, 0.5 and 0.8 respectively. As the main focus of this study, five occurrence percentage configurations are selected for analysis. Lastly, each treatment is examined during normal conditions and when subject to PNS attacks in order to baseline the QKD system's performance and ability to detect PNS attacks. Note, the decoy state protocol does not prevent the attack, it merely detects it.  
All other design and configuration settings are held constant (described in Section 3.3).  
For this study, a full factorial design was selected, as it is relatively easy to simulate all 80 treatments once the experimental factors are well understood. In order to characterize the modeled system's behavior well across all 80 configurations and make statistically significant conclusions, 1000 simulation runs were executed for each treatment using the DoD's High Performance Computing Modernization Program at Wright-Patterson Air Force Base. In particular, the model was packaged as a single executable application with a series of command line parameters, to account for the design of Table 5, and executed in parallel over 1024 cores for a total of 80,000 simulation runs for a total of nearly 200,000 h of processor time.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Operational Distance** & **Signal MPN** & **Decoy MPN** &
\begin{tabular}{c} **Occurrence Percentage** \\ **(Signal/Decoy/Vacuum)** \\ \end{tabular} & **PNS Attack** \\ \hline
20 km & 0.5 & 0.1 & 60/30/10 & No \\
50 km & 0.8 & 0.2 & 70/20/10 & Yes \\ — & — & — & 80/10/10 & — \\ — & — & — & 90/5/5 & — \\ — & — & — & 99/0.5/0.5 & — \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental Design.  
Regarding this experimental design, it is important to note that 20 km does not necessarily provide a sufficient loss budget for [PERSON] to conduct PNS attacks without negatively impacting [PERSON]'s expected detection rate [59]. This is because [PERSON] introduces loss on the quantum channel as she blocks all the single photon pulses sent by [PERSON]. For example, [PERSON] introduces \(\sim\)7.4 dB loss against an MPN of 0.5, whereas the 20 km link only provides a \(\sim\)4 dB loss budget for [PERSON] to take advantage of with her lossless quantum teleportation channel. Despite this constraint, analyzing the decoy state protocol's ability to detect PNS attacks at this distance is desirable because many implementations have operational distances of 15-25 km as noted in Table 4. Moreover, if [PERSON] is able to insert herself on the quantum channel before protocol calibration, her presence would go unnoticed with respect to loss and key rate.