# Loop-Back Quantum Key Distribution (QKD) for Secure and Scalable Multi-Node Quantum Networks
## 2 Loop-Back QKD in a Linear Topology
### Hybrid Loop-Back-BB84 QKD
Key reconciliation and privacy amplification. -- [PERSON] and [PERSON] reconcile their keys using the sifting cases. -- They apply error correction and privacy amplification to generate two secure keys: one from the direct transmission (\(k_{ab}\)) and another from the full round trip (\(k_{ab}\)). -- The final key is obtained by applying an XOR operation to \(k_{ab}\) and \(k_{aba}\) to enhance security. Figure 3: Optical setup for Loop-Back QKD in reflection mode. The elements labeled \(F_{a}\), \(F_{b}\), and \(F_{e}\) in the upper schematic correspond to the polarizers used by [PERSON], [PERSON], and a potential eavesdropper ([PERSON]), respectively. The beam splitter (BS) directs the incoming pulse toward either a transparent path or a reflective path. In the reflective path, a dielectric mirror (or a Faraday retroreflector) ensures that the pulse is returned to its source while preserving its quantum properties. The optical coupler reinjects the processed pulse into the fiber, minimizing loss and maintaining coherence. The presence of \(F_{e}\) illustrates a possible interception attempt by an adversary attempting to manipulate the quantum states. The lower schematic shows the end-to-end execution of the protocol: [PERSON] sends the state \(0_{Z}\) to [PERSON], who polarizes it using the \(X\) basis, producing \(1_{X}\). When this state arrives at [PERSON]’s station, she measures it using the \(Z\) basis. In this example, she obtains \(1_{Z}\), allowing her to infer [PERSON]’s choice of the \(X\) basis. Table 1 presents the probability distribution of the Loop-Back protocol in an ideal quantum channel. Table 3, on the other hand, illustrates the distribution in the presence of [PERSON] conducting a MitM attack on the quantum channel. Based on these results, we now describe the second method for detecting the presence of [PERSON] in the quantum channel. Table 4 presents a comparison of the performance of the BB84 and Loop-Back protocols. The column labeled \(Th_{ab}\) is the throughput of the protocol, i.e., the total number of events eligible for distillation. As shown in the BB84 protocol, \(Th_{ab}\) remains unchanged before and after the attack. Therefore, it is necessary to sacrifice a portion of the bits to measure the error rate of the protocol. In contrast, the Loop-Back protocol exhibits a \(12.5\%\) increase in \(Th_{ab}\), meaning that no bits need to be sacrificed to measure the error rate. Instead, it is sufficient to evaluate \(Th_{ab}\) directly for the protocol. As a third measure to detect the MitM attack, [PERSON] can determine [PERSON]'s presence in the channel because [PERSON] is unable to control the delay \(\Delta t\) caused by the attack. Although \(\Delta t\) may be very small, [PERSON] introduces a constant delay of \(2\Delta t\) in the \(ABA\) link. If [PERSON] measures the round-trip time of the pulse using a sufficiently accurate clock, she will notice this delay compared to the value set during the initial system calibration, thereby concluding with the presence of [PERSON]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **Result** & **Prob.