## 3 Network Model
### QKD Protocol, Model and Related Definitions  
Within the entire network architecture of the CPSR-HQKDN scheme, Quantum Key Distribution (QKD) protocols play a crucial role in data packet encryption [30]. This scheme employs a collaborative deployment of the BB84 protocol and the MDI-QKD protocol to allocate distinct paths for data packets based on varying security requirements. Illustrated in Figures 2 and 3, the basic principles of point-to-point communication using the BB84 protocol and MDI-QKD protocol in the Quantum Key Distribution (QKD) links are presented. The BB84 Protocol: Firstly, both parties need to prepare a key. The sender ([PERSON]) and the receiver ([PERSON]) each prepare a key, which can be generated randomly as a bit sequence (e.g., 01 sequence). Then, [PERSON] sends a sequence of quantum bits through a quantum channel to [PERSON], where each bit represents a randomly chosen quantum state, such as horizontally/vertically or diagonal/anti-diagonal polarized photons. Upon receiving the quantum bits, [PERSON] randomly chooses a set of measurement bases. Each measurement basis corresponds to a different polarization direction of the quantum bit. [PERSON] measures the received quantum bits using the selected measurement bases and records the outcomes. It should be noted that due to the nature of quantum states, the measurement outcomes are affected by uncertainty. [PERSON] then publicly announces to [PERSON] the information about the selected measurement bases, but does not disclose the specific measurement outcomes. At this point, [PERSON] and [PERSON] confirm through classical communication that they have indeed used the same measurement bases. This step is crucial to ensure the subsequent comparison  
Figure 2: Basic principle diagram of using the BB84 protocol in the QKD link. of the bit values' meaning. [PERSON] and [PERSON] compare their measured outcomes, and based on the previously confirmed measurement basis information, they determine which outcomes are trustworthy. These trustworthy outcomes are used to generate the key. Next, [PERSON] and [PERSON] calculate the bit-error rate based on the publicly compared partial bit values. If the error rate exceeds a specific threshold, there may be a risk of eavesdropping or communication errors. This will determine whether the current key is retained. Finally, [PERSON] and [PERSON] extract the final key through an error correction protocol. This protocol can be achieved by using error correction codes to ensure the security of the key, even at a limited error rate. After obtaining the key, [PERSON] and [PERSON] can store it in the key pool [31]. MDI-QKD Protocol: As shown in Figure 3,Alice and [PERSON] use phase randomization to prepare four BB84 states with weak coherent light pulses, including horizontal polarization state \(|H\rangle\), vertical polarization state \(|V\rangle\), diagonal polarization state \(|+\rangle=\sqrt{2}(|H\rangle+|V\rangle)\), and \(|-\rangle=\sqrt{2}\) (\(|H\rangle-|V\rangle)\). They send these states through a quantum channel to a third party, [PERSON], and announce the encoding basis they used. [PERSON] performs Bell state measurements after receiving two qubits and publicly announces the successful measurement results. Meanwhile, [PERSON] and [PERSON] select to flip or not flip their bits on hand for the parts where they use the same basis as [PERSON]'s to obtain positively correlated data. For example, if [PERSON] measures \(|HV\rangle\), [PERSON] and [PERSON] choose to flip their vertical polarization state \(|V\rangle\). To obtain the gain and error rate of the single-photon portion, [PERSON] and [PERSON] use the decoy-state method. They each choose a random basis and send it to each other through the quantum channel. After receiving the basis, the other party measures its polarization state and informs the result. Based on these results, [PERSON] and [PERSON] can calculate the gain and error rate of the single-photon portion.