Act as a university professor lecturing a graduate-level physics class. Provide a detailed technical explanation of the BB84 Quantum Key Distribution protocol. Start by defining the four polarization states and the two bases. Then, mathematically demonstrate how an intercept-resend attack by an eavesdropper (Eve) introduces a quantum bit error rate (QBER) of at least 25%, which alerts Alice and Bob to her presence. Finally, describe the process of sifting and error correction used to generate the final secure key.