Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 10D / b

Run the perfect discriminator on the supplied state and record whether the result is $i=0$ or $i=1$. For each $i$, choose a unitary $V_i$ satisfyingwhich is possible by extending $|{\varphi }_i⟩$ to an orthonormal basis. Prepare two fresh systems in $|0⟩|0⟩$ and, controlled by the classical outcome $i$, apply $V_i\otimes V_i$. The output isThe discriminator may destroy its input; the two freshly prepared outputs still implement cloning on this known pair. This is the construction that perfect discrimination implies cloning for a known state family.