What theorem states that an unknown quantum state cannot be perfectly copied?

The theorem stating that an unknown quantum state cannot be perfectly copied is the no-cloning theorem.

In classical computing, copying information is straightforward: a bit can be duplicated without changing its value. Quantum states behave differently. The no-cloning theorem shows that no universal physical operation can take an arbitrary unknown state and produce two perfect copies of it.

The result follows from the linearity of quantum mechanics. If a copying machine worked for two possible states, applying the same operation to a superposition would generally produce an entangled state rather than two independent copies of the original. The theorem was formulated independently by W. K. Wootters and W. H. Zurek, and by Dennis Dieks, in 1982.

No-cloning does not mean quantum information can never be copied in any form. Known orthogonal states can be copied, and approximate or imperfect cloning is possible. What is forbidden is perfect copying of an arbitrary unknown state. Quantum teleportation also does not violate the theorem: the original state is destroyed during the protocol, so it is transferred rather than duplicated.

The theorem is central to quantum cryptography because an eavesdropper cannot silently copy an unknown quantum key state. It is unrelated to the Pauli exclusion principle, which governs the occupancy of identical fermion states.