Theorem: x(1 - x) - (x - x^2) = 0 (cloning quadratic identity, only roots {0, 1})

Theorem (no-cloning quadratic-zero canonical): for inner product x = <phi|psi> in [0, 1], the cloning condition x = x^2 has factorisation x(1 - x) = 0, with the only solutions being x = 0 (orthogonal states) and x = 1 (identical states).…