= Solution
Let Alice and Bob share the <Bell state>
$$
|\Phi^+\rangle
=\frac{|00\rangle+|11\rangle}{\sqrt2}
=\frac{|++\rangle+|--\rangle}{\sqrt2}.
$$
Alice may measure in the computational basis, remotely preparing Bob's ensemble $\{|0\rangle,|1\rangle\}$, or in the Hadamard basis, preparing $\{|+\rangle,|-\rangle\}$. Without her outcome, both ensembles have density matrix $I/2$, as no-signalling requires.
If Bob could clone all four states, the resulting two-qubit ensembles would be
$$
\frac12(|00\rangle\langle00|+|11\rangle\langle11|)
$$
and
$$
\frac12(|++\rangle\langle++|+|--\rangle\langle--|).
$$
They are distinguishable: a $Z\otimes Z$ measurement is perfectly correlated for the first and only equally likely correlated or anticorrelated for the second. Bob could infer Alice's basis choice instantaneously, violating no-signalling. Thus no-signalling implies no-cloning for this set.
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