= No-cloning theorem
{wiki}
No deterministic quantum operation can make two perfect copies of every unknown <pure state>. For a proposed <unitary operator> acting with a fixed blank and environment, preservation of inner products gives $c=c^2 e$, where $c$ is the input overlap and $|e|\leq1$ is the overlap of final environment states. Nonorthogonal distinct states have $0<|c|<1$, contradicting this equality. The <no-cloning theorem for two pure states> is its elementary two-state form.
Back to article page
