No unitary can copy arbitrary unknown quantum state: U|ψ⟩|0⟩ = |ψ⟩|ψ⟩ fails by linearity. Foundation of quantum cryptography.
No-cloning theorem
Related concepts
- Heisenberg uncertainty principle
- Quantum error correction (Shor/Steane codes)
- No-cloning: ⟨φ|ψ⟩ = √2/2 forbids perfect copy; BH fidelity 5/6, shortfall 1/6
- Shor's algorithm (1994)
- Grover's algorithm (1996)
- BB84 (Bennett-Brassard 1984)
- Quantum supremacy (Arute 2019)
- Teleportation (Bennett 1993)
- Distillation (Bennett 1996)