Quantum Key Distribution

Unbreakable Encryption

Quantum Key Distribution (QKD) uses quantum mechanics to share a secret key between two parties — with the guarantee that any eavesdropping is physically detectable.

The BB84 protocol (Bennett & Brassard, 1984) works as follows:

1. Alice prepares qubits in one of two bases:

   • Z basis (computational): $0 o |0 angle$, $1 o |1 angle$
   • X basis (diagonal): $0 o |+ angle$, $1 o |- angle$

2. Bob measures each qubit in a randomly chosen basis.

3. Sifting: Alice and Bob publicly announce which bases they used. They keep only the results where their bases matched — these form the secret key.

When bases match, measurement is deterministic: Bob gets exactly what Alice sent. When they don't match, the result is random and discarded.

def sift_keys(alice_bits, alice_bases, bob_bases):
    alice_key, bob_key = [], []
    for a_bit, a_base, b_base in zip(alice_bits, alice_bases, bob_bases):
        if a_base == b_base:  # Bases matched!
            alice_key.append(a_bit)
            bob_key.append(a_bit)  # Deterministic when bases agree
    return alice_key, bob_key

Your Task

Implement sift_keys(alice_bits, alice_bases, bob_bases) that returns the matching key bits for Alice and Bob.