= Solution
{c}
\b[No: the advertised pure joint state is incompatible with these marginals.] Their eigenvalue multisets are $\{0.9,0.1\}$ and $\{0.7,0.3\}$, which differ. Part <3/a> shows that a bipartite pure state must give the same nonzero <Schmidt spectrum> on both sides.
This excludes Eve's purity claim, not every possible joint state or every possibility of entanglement. A mixed state can have unequal marginal spectra; the product $\rho_A\otimes\rho_B$, for example, has exactly the stated marginals.
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