Why BB84 is Secure
BB84 exploits two fundamental quantum properties:
1. No-Cloning Theorem: An unknown quantum state cannot be perfectly copied. Eve cannot copy Alice's qubits to measure them later without disturbing the originals.
2. Measurement Disturbs State: When Eve measures a qubit in the wrong basis, she irreversibly changes its state. If Alice sent |0> in the + basis and Eve measures in the x basis, the qubit collapses to either |/> or |\> — then when Bob measures it, he gets a random result even if he chose the right basis.
Detection: Alice and Bob sacrifice a portion of their shared key to check for errors. Without Eve, error rate is ~0%. With Eve intercepting all qubits, error rate is ~25%. Any significant error rate reveals eavesdropping, and they discard the key.
Key rate: On average, Alice and Bob's bases match 50% of the time, so the raw key is half the transmitted bits. After error checking, the usable key is slightly shorter.