# 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  
The Loop-Back protocol can be integrated with BB84 to create a hybrid configuration that enhances security against MitM. Under this protocol, [PERSON] may modify the state returned to [PERSON] according to the following schemes: (1) polarize the state in one of the bases \((X,Z)\), (2) leave the state unpolarized (return it as received), or (3) measure it in one of the bases \((X,Z)\). In essence, this setup combines a traditional BB84 protocol with an inverted protocol executed by [PERSON]. Finally, the states returned unaltered by [PERSON] to [PERSON] allow her to verify the integrity of the quantum channel. [PERSON] and [PERSON] have synchronized systems and are aware of the quantum channel's losses and error rate (\(e\)). The system requires [PERSON] to use a detection setup identical to [PERSON]'s, and [PERSON] knows the round-trip time of a quantum pulse. The upper schematic in Figure 3 shows the optical setup the protocol, where [PERSON] first acts as the transmitter and subsequently as the receiver. The communication occurs via the same optical channel in both directions, as indicated in the figure. The solid line denotes the initial transmission from [PERSON] to [PERSON], while the faded line represents the return transmission from [PERSON] to [PERSON] at a later stage. [PERSON] performs an intermediate measurement using a randomly selected basis, after which the signal continues to [PERSON], who also selects a basis for detection. It is important to highlight that [PERSON]'s polarizers, labeled \(F_{\mathrm{p}_{1}}\) and \(F_{\mathrm{p}_{2}}\) in the figure, can be reduced to a single polarizer, as illustrated in the lower schematic of Figure 3. This reduction arises from the fact that [PERSON] either measures the incoming pulse in a chosen basis or polarizes it before retransmission, but he cannot perform both operations simultaneously. Consequently, a single polarizer suffices to fulfill both functions. Similarly, for [PERSON], the polarizer \(F_{a_{1}}\) is identical to \(F_{a_{2}}\), as required by the structure of the protocol. This optimization simplifies the optical setup while ensuring the integrity of the quantum state transmission is preserved. During a MitM attack, [PERSON] installs two devices: one that measures the state sent by [PERSON] and allows her to resend a pulse to [PERSON] with the polarization of the result obtained from her measurement, and another that measures the state returned by [PERSON], which [PERSON] then forwards to [PERSON]. Protocol Description [PERSON] and [PERSON] follow these steps:  
1. [PERSON] randomly selects a basis \(B_{A}\in\{X,Z\}\) and prepares a state \(\psi\), such that \(\psi\in\{0_{Z},1_{Z},0_{X},1_{X}\}\), and sends \(\psi\) to [PERSON]. 2. [PERSON] applies one of three possible operations: 1. Polarize and resend: [PERSON] selects a basis \(B_{B}\in\{X,Z\}\), polarizes the state accordingly, and sends it back to [PERSON]. 2. Forward unchanged: [PERSON] does not modify the state and simply returns it as received. 3. Measure the state: [PERSON] measures \(\psi\) in a randomly chosen basis \(B_{B}\) (\(X\) or \(Z\)), collapsing the quantum information. [PERSON] measures the returned state. If [PERSON] did not discard the state in case (3), [PERSON] measures it using her original basis \(B_{A}\). 4. [PERSON] announces his operations. Over a classical channel, [PERSON] reveals which of the three operations he applied. If he performed a measurement (as described in operation (3)), he also discloses the basis \(B_{B}\) he used. 5. [PERSON] classifies the results: -- Sifting cases: If [PERSON]'s measurement result is orthogonal to her original state (\(\
eg\psi\)), she can deduce the basis used by [PERSON]. These cases are used for key generation. -- Channel verification cases: If [PERSON] returned the state unchanged, [PERSON] uses these events to monitor the quantum channel's error rate. Deviations from the expected error rate may indicate the presence of an eavesdropper, serving as the first strategy for attack detection. 6.