Quantum Key Exchange
Explained in Detail

Alice starts by generating:

• A random sequence of bits (0s and 1s)
• A random sequence of bases (+ or ×) for each bit

She encodes each bit in the corresponding quantum basis:

• + basis: 0 → |0⟩, 1 → |1⟩
• × basis: 0 → |+⟩, 1 → |-⟩

Alice sends the encoded quantum states to Bob through a quantum channel (typically photons in optical fiber):

• Each quantum state is fragile - any measurement will disturb it
• The transmission is one-way (Alice→Bob)
• Quantum no-cloning theorem prevents perfect copying

Bob measures each quantum state using randomly chosen bases:

• When basis matches Alice's: Correct bit result
• When basis doesn't match: Random 50/50 result

Example outcomes:

Alice and Bob publicly compare their bases (not the bits!):

• They discard all bits where bases didn't match
• The remaining bits form the raw key
• About 50% of bits are typically kept

Example with 4 qubits:

To detect eavesdropping:

• Alice and Bob sacrifice some key bits by comparing them publicly
• If any bits disagree, Eve must have measured them
• No errors means either no Eve or she guessed all bases correctly

Security comes from:

• Quantum uncertainty - Eve can't clone states
• Randomness - Eve can't predict which bases to use
• Error detection - Any interference leaves traces

With a verified secure key, Alice and Bob can communicate:

• One-Time Pad (XOR): Perfect secrecy when key length ≥ message length
• AES Encryption: For longer messages with key expansion

XOR Example:

Message:  H    e    l    l    o
ASCII:   01001000 01100101 01101100 01101100 01101111
Key:     01011010 10100101 11010011 00101101 10011010
---------------------------------------------------- XOR
Cipher:  00010010 11000000 10111111 01000001 11110101

Only with the exact same key can Bob decrypt the message.