Quantum Cryptography

Quantum cryptography primarily encompasses Quantum Key Distribution (QKD) and, more theoretically, quantum digital signatures and quantum secure direct communication. QKD protocols, like BB84, utilize properties of photons to establish a shared secret key between two parties (Alice and Bob). In BB84, Alice encodes bits onto photon polarization states (e.g., rectilinear basis $\{|0\rangle, |1\rangle\}$ and diagonal basis $\{|+\rangle, |- angle\}$), where $|+\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ and $|-\rangle = \frac{1}{\sqrt{2}}(|0\rangle - |1\rangle)$. Bob randomly chooses a basis to measure each incoming photon. After transmission, Alice and Bob publicly compare their basis choices. They discard measurements where bases didn't match and keep the rest, forming a raw key. Any eavesdropper (Eve) attempting to intercept and measure the photons will inevitably disturb their quantum state due to the no-cloning theorem and the probabilistic nature of quantum measurement. This disturbance introduces errors into the raw key, which Alice and Bob can detect through error rate analysis and privacy amplification techniques. Post-processing steps like error correction (e.g., Cascade protocol) and information reconciliation are crucial to distill a secure, shared secret key from the noisy quantum channel. Advanced protocols like E91 utilize entanglement to enhance security. The security of QKD is rooted in the fundamental laws of physics, not computational complexity, making it resistant to future advances in computing, including quantum computers.