No-cloning theorem: U|psi>|0> = |psi>|psi> for all psi forces <phi|psi> in {0, 1}

No-cloning framework via inner-product preservation (Wootters-Zurek 1982 Nature 299, 802; Dieks 1982 Phys Lett A 92, 271). Setup: a universal quantum cloner would be a unitary U on H_input tensor H_blank tensor H_ancilla satisfying U|psi>…