Quantum Key Distribution — Full Security Proof
Stub. A rigorous, multi-lecture treatment of QKD beyond the protocol sketch: the problem setup and indistinguishability of the relevant quantum states, a sequence of failed/partial attempts motivating the real protocol, the adversarial view and the sampling game that captures an eavesdropper's best strategy, agreement and secrecy intuition, classical sampling/estimation theorems relating test and generation subsets, relating quantum to classical sampling, and finishing the protocol with error correction and privacy amplification.
Corresponds to Chapters 9.5–9.6 and 10–12.2. Goes far beyond the one-paragraph BB84 sketch in quantum-information-and-cryptography (that note’s home for the basic “measurement disturbs the state” intuition) with a full security proof. Sets up the protocol precisely and the indistinguishability property it relies on, then walks through a sequence of naive protocol attempts and why each fails, before analyzing the real protocol from the adversarial view: modeling the eavesdropper’s optimal strategy as a sampling game. Formalizes the intuition for why honest parties agree on a key and why it’s secret from an eavesdropper via classical sampling and estimation theorems (relating statistics on a test subset of qubits to the generation subset actually used for the key, the technical core that quantum measurement disturbance (quantum-measurement-and-steering) gets converted into), and a theorem relating quantum sampling bounds back to classical ones. Closes the protocol with error correction (reconciling small discrepancies between the parties’ raw keys) and privacy amplification (shrinking the key to remove any residual information the sampling bounds show could have leaked).
Outline (TODO — flesh out each)
- Problem setup
- Indistinguishability
- Protocol attempts 0, 1, 2 — why each fails or is incomplete
- An alternative perspective
- The adversarial view
- The sampling game
- Agreement: intuition
- Secrecy: intuition
- Classical sampling and estimation theorems
- Relating quantum sampling to classical sampling
- Error correction in QKD
- Privacy amplification in QKD