Why QKD is Unconditionally Secure

Why QKD is Unconditionally Secure

BB84's security is not based on computational assumptions: it is based on the laws of quantum physics. Even a computationally unbounded adversary cannot break it. This is a fundamentally different security guarantee from RSA, AES, or any algorithm whose security reduces to "this problem is hard to compute."

Information-Theoretic vs Computational Security

Computational security: An algorithm is secure if no efficient (polynomial-time) algorithm can break it. RSA is computationally secure against classical computers: but Shor's algorithm shows it is not computationally secure against quantum computers.

Information-theoretic security: An algorithm is secure regardless of the attacker's computational power. The one-time pad provides this for encryption; QKD provides it for key distribution.

The combination of QKD (for key distribution) + OTP (for encryption) is the only known communication system with end-to-end information-theoretic security.

The No-Cloning Theorem

The foundation of QKD security is the no-cloning theorem: an unknown quantum state cannot be perfectly copied.

Proof sketch: Suppose a unitary U could clone states: U(|ψ⟩|0⟩) = |ψ⟩|ψ⟩ for all |ψ⟩. Applying this to a superposition:

U((|0⟩+|1⟩)|0⟩) = U(|0⟩|0⟩) + U(|1⟩|0⟩) = |0⟩|0⟩ + |1⟩|1⟩

But linearity requires:

U((|0⟩+|1⟩)|0⟩) = (|0⟩+|1⟩)(|0⟩+|1⟩) = |0⟩|0⟩ + |0⟩|1⟩ + |1⟩|0⟩ + |1⟩|1⟩

These are different states: contradiction. No such U can exist.

Implication for QKD: Eve cannot intercept Alice's qubit, copy it, and forward the copy to Bob. She must choose between intercepting (and disturbing the state) or forwarding (and learning nothing). She cannot do both.

Measurement Disturbance

A complementary principle: measuring a quantum state in an incompatible basis disturbs it. If Alice sends |+⟩ (X-basis state) and Eve measures in the Z-basis, she gets a random result and the state collapses to |0⟩ or |1⟩. When she forwards this to Bob, the state is no longer |+⟩. When Bob measures in the X-basis, he gets a random result instead of the deterministic +1 he would have gotten from |+⟩.