No-cloning: ⟨φ|ψ⟩ = √2/2 forbids perfect copy; BH fidelity 5/6, shortfall 1/6

Sympy-exact symbolic witness of the Wootters-Zurek 1982 / Dieks 1982 no-cloning theorem + the Bužek-Hillery 1996 universal cloner bound. Step 1 — impossibility witness: for |φ⟩ = |0⟩, |ψ⟩ = (|0⟩ + |1⟩)/√2, overlap ⟨φ|ψ⟩ = 1/√2 = √2/2; a…