No-cloning theorem

The no-cloning theorem states that no physical operation can perfectly copy every possible unknown quantum state. It follows from the linearity of quantum mechanics.

Quantum state: A mathematical description of a quantum system’s possible measurement outcomes and their probabilities. The theorem concerns copying states, not copying classical descriptions of them.
Quantum teleportation: A protocol that transfers an unknown quantum state using shared entanglement and classical communication. Teleportation transfers the state rather than leaving an intact original alongside a perfect copy.
Classical information: Information encoded in distinguishable classical alternatives, such as bits with values zero and one. Classical bits can be copied perfectly, unlike arbitrary unknown quantum states.
William K. Wootters: An American theoretical physicist whose work helped establish foundational results in quantum information. Wootters co-authored an influential 1982 proof of the impossibility of universal quantum copying.
Quantum superposition: A quantum state formed as a coherent combination of possible states. Linearity requires a copier to preserve superpositions, which defeats copying two distinct basis states.
Quantum key distribution: A family of cryptographic protocols that establishes secret keys using quantum states and measurements. Eavesdropping cannot copy arbitrary transmitted states without detectable disturbance.
No-broadcasting theorem: A theorem stating that noncommuting quantum states cannot be broadcast while preserving their original local states. It generalizes the restriction from making identical copies to distributing states with correct marginals.
Wojciech H. Zurek: A Polish-American theoretical physicist known for work on quantum measurement, decoherence, and quantum information. Zurek independently formulated the no-cloning result with Wootters in 1982.
Linearity of quantum mechanics: The principle that quantum evolution maps linear combinations of states to corresponding linear combinations of evolved states. Applying linear evolution to candidate copies of basis states yields the contradiction at the proof’s core.
Quantum error correction: Methods that protect quantum information by encoding it across multiple physical systems. Error-correcting codes add redundancy without making forbidden copies of an unknown encoded state.

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