# Loop-Back Quantum Key Distribution (QKD) for Secure and Scalable Multi-Node Quantum Networks
## 3 Loop-Back QKD in a Ring Topology  
The Loop-Back QKD protocol extends naturally to multiuser scenarios, enabling secure key distribution in a network setting. Unlike conventional QKD protocols designed for point-to-point communication, this approach supports an arbitrary number of users by leveraging a bidirectional optical ring. In each round, a designated node transmits quantum states while the other nodes interact with the pulses according to predefined rules. At any given time, only one transmission direction is active, randomly determined by the transmitting node to introduce additional security against eavesdropping. Each participating node can perform one of the following actions upon receiving a pulse:  
* Transmit and Measure: The designated node sends a polarized quantum state into the ring and later measures the pulse after it has either been reflected or has completed a full circuit around the ring if all intermediate nodes act transparently. * Reflect with polarization: Apply a unitary transformation in a randomly chosen basis (\(X\) or \(Z\)) and return the pulse to the sender. * Forward without polarization: Preserve the pulse's original state and transmit it unchanged. A fundamental rule governs the interactions: a node can either reflect the pulse with polarization or forward it without polarization, regardless of the pulse's incoming direction. Since a pulse propagates through the network, it continues traveling through transparent (forwarding) nodes until it encounters the first reflecting node (see Figure 4). At this point, the pulse is returned to the sender, allowing them to establish a correlated result with the reflecting node. This structured interaction ensures that sifting occurs efficiently without requiring additional coordination among intermediate nodes. This mechanism introduces three key security properties. First, since the pulse direction is randomized, an eavesdropper cannot predict or manipulate the transmission path without introducing detectable anomalies. Second, because the reflection process occurs independently of the pulse's initial direction, an adversary cannot infer information based on routing behavior. Third, the protocol ensures that a number of pulses will always return to their origin after completing the full ring, preserving the same polarization state in which they were originally sent. To illustrate the protocol's operation in a networked environment, we consider the simplest multiuser scenario involving three nodes: A, B, C and D. These nodes are interconnected in a ring topology, allowing bidirectional communication as indicated in Figure 4. In this network, some nodes B, C act as transparent forwarders, while D applies polarization and reflection. The protocol generalizes to any number of users by maintaining the sequential turn system and the rule for polarization and forwarding. The synchronization of turns and direction selection are easily managed through classical communication channels. Key reconciliation relies on the progressive establishment of correlations between nodes over multiple rounds of transmission. In a given round, A transmits, and the first reflecting node is D, establishing a correlation between them. In subsequent rounds, different nodes take turns transmitting, each time forming a new correlation with the first encountered reflecting node. After a sufficient number of rounds, all nodes in the ring will have established shared correlations. In the ideal case, where no errors occur, these correlations enable the distillation of a global group key among all nodes. Alternatively, depending on network conditions and security requirements, subgroups of nodes (e.g., {A, D}, {A, B, D},...) can derive independent shared keys based on their accumulated correlations. A full characterization of the key reconciliation process requires experimental validation or numerical simulation to determine the efficiency of correlation establishment and the impact of quantum channel noise on key rates.