= Solution
Let $U(t)=e^{-itH}$. Define the second initial state by $|\widetilde\psi_0\rangle=U(t)^\dagger|\psi_2\rangle$, while $|\psi_0\rangle=U(t)^\dagger|\psi_1\rangle$. The <unitary time evolution> preserves their <inner product>:
$$
\boxed{\langle\widetilde\psi_0|\psi_0\rangle=\langle\psi_2|UU^\dagger|\psi_1\rangle=0.}
$$
Both initial states are normalized and evolve to the chosen final pair. This supplies the orthogonal partner needed for <topological quantum order>. The remaining requirement is <local indistinguishability>, which is proved in the next condition's solution.
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