= Solution
Apply the hypothetical <quantum cloning> device repeatedly to obtain $N$ copies of the unknown state. If $c=|\langle\phi|\psi\rangle|<1$, the two possibilities are
$$
|\phi\rangle^{\otimes N},
\qquad |\psi\rangle^{\otimes N},
$$
whose overlap has modulus $c^N$. For equal prior probabilities, the <Helstrom-Holevo bound> gives optimal success probability
$$
P_N=\frac12\left(1+\sqrt{1-c^{2N}}\right)
\longrightarrow1.
$$
Thus, for any $\varepsilon>0$, sufficiently many clones permit success probability above $1-\varepsilon$. Orthogonal states already have $c=0$ and can be distinguished perfectly. This is <clone-assisted asymptotic state discrimination>.
Here distinct states means distinct rays. Vectors differing only by a global phase represent the same <quantum state> and cannot be distinguished.
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