Cryptography

Quantum Key
Distribution

Using the laws of quantum mechanics to establish cryptographic keys with information-theoretic security. Any eavesdropping attempt physically disturbs the quantum states being transmitted — making interception detectable by the communicating parties.

BB84 Protocol E91 Protocol No-Cloning Theorem Information-Theoretic Security QBER Practical Limitations

Security from Physics, Not Mathematics

Classical cryptographic key exchange (Diffie-Hellman, RSA) derives its security from the assumed computational difficulty of mathematical problems — problems that Shor's algorithm would render trivial on a sufficiently powerful quantum computer.

QKD takes a fundamentally different approach. Its security is grounded in the laws of physics: the Heisenberg Uncertainty Principle ensures that measuring a quantum state disturbs it, and the No-Cloning Theorem guarantees that an unknown quantum state cannot be copied. Any eavesdropper who intercepts the quantum channel necessarily introduces detectable errors.

The security of QKD is information-theoretic (sometimes called "unconditional") — it holds against an adversary with unlimited computing power, including future quantum computers.

The BB84 protocol. Alice encodes each bit in one of two conjugate bases (rectilinear or diagonal). Bob measures each qubit in a randomly chosen basis. After transmission they publicly compare bases (not values) and retain only measurements where bases matched — the sifted key. Source

How BB84 Works

Step 1 — Preparation: Alice randomly selects a bit value (0 or 1) and a basis (rectilinear {|0⟩,|1⟩} or diagonal {|+⟩,|−⟩}) for each qubit she sends to Bob over a quantum channel.

Step 2 — Measurement: Bob independently and randomly chooses a measurement basis for each qubit. When he uses the same basis as Alice, he always measures the correct bit. When the bases differ, his result is random.

Step 3 — Sifting: Alice and Bob publicly announce which bases they used (but not their bit values) via a classical channel. They discard all bits where their bases didn't match — roughly 50%. The remaining bits form the sifted key.

Step 4 — Error estimation: They compare a random sample of their sifted key bits publicly to estimate the Quantum Bit Error Rate (QBER). If QBER exceeds ~11%, the channel is considered compromised and the key is discarded.

Step 5 — Privacy amplification: Classical post-processing (error correction + privacy amplification) distils the remaining bits into a shorter, provably secure final key.

Entanglement-Based QKD

Approach: Rather than Alice sending prepared qubits, a source distributes pairs of entangled photons — one to Alice, one to Bob. The correlations of their measurements (in randomly chosen bases) produce a shared secret key.

Security mechanism: E91 uses Bell inequality tests to authenticate the quantum channel. Quantum mechanics predicts that entangled measurements violate the CHSH inequality (|S| = 2√2 ≈ 2.83), while any classical or eavesdropped system is bounded by |S| ≤ 2. A deviation from quantum predictions reveals an adversary.

Advantage — Device Independence: In principle, E91's security does not require trusting the hardware, since the Bell test itself certifies quantum behaviour. This makes it the theoretical basis for device-independent QKD.

Feature BB84 E91
Physical basis Superposition / uncertainty principle Entanglement / Bell inequalities
Hardware Single-photon source + polariser Entangled photon pair source
Eavesdropping detection Elevated QBER Bell inequality deviation
Device independence No Possible in principle
Deployment maturity Commercially available (Toshiba, ID Quantique) Experimental / satellite demonstrations
China's Micius satellite (launched 2016) demonstrated intercontinental QKD over 7,600 km via satellite relay — circumventing the optical fibre distance limitation with free-space quantum channels between ground stations. Source
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Distance Limits

Photon loss in optical fibre (~0.2 dB/km) limits practical QKD range to around 100–200 km without quantum repeaters, which remain an unsolved engineering challenge.

Low Key Rates

Current systems generate keys at kilobits to megabits per second — insufficient for high-throughput applications. AES key exchange is orders of magnitude faster.

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Side-Channel Attacks

The protocol may be secure in theory, but hardware implementations can be exploited — e.g. detector blinding attacks manipulate photon detectors. Real-world security requires careful engineering beyond the protocol itself.

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Trusted Relay Nodes

Long-distance QKD networks rely on trusted intermediate nodes (e.g. China's 2,000 km Beijing–Shanghai link). Each node is a potential physical vulnerability if compromised.

The No-Cloning Theorem: Quantum mechanics forbids copying an unknown quantum state. There is no unitary operation U such that U|ψ⟩|0⟩ = |ψ⟩|ψ⟩ for all |ψ⟩. This physical fact is the foundation of QKD security — an eavesdropper cannot intercept and re-transmit a qubit without disturbing it.