= Solution
A compression scheme consists of <quantum channels>
$$
\mathcal C_n:\mathcal B(\mathcal H^{\otimes n})\to\mathcal B(\mathcal K_n),\qquad\mathcal D_n:\mathcal B(\mathcal K_n)\to\mathcal B(\mathcal H^{\otimes n}),
$$
where each is a <CPTP map>. The <Hilbert space> $\mathcal K_n$ is the compressed register. Its block rate in qubits per source qubit is $R_n=n^{-1}\log_2\dim\mathcal K_n$, with asymptotic rate $R=\limsup_nR_n$ (or the limit when it exists).
Use the <squared quantum fidelity> convention for the ensemble overlap:
$$
\boxed{F_n=\sum_kp_k^{(n)}\langle\Psi_k^{(n)}|\mathcal D_n\mathcal C_n(|\Psi_k^{(n)}\rangle\langle\Psi_k^{(n)}|)|\Psi_k^{(n)}\rangle.}
$$
This definition tests preservation of the emitted vectors themselves, including nonorthogonal ones; preserving only their classical labels would be a different task. \b[The scheme is reliable when $F_n\to1$ as $n\to\infty$.] This is the ensemble-average criterion for <reliable quantum source compression>. A square root is not taken in this definition, even though an unsquared convention is also used for <quantum fidelity>.
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