= Typical-subspace compression with a failure flag
{title2=$F_e(\pi^{\otimes n},\mathcal N_n)\geq[\operatorname{Tr}(\pi^{\otimes n}\Pi)]^2$}
Measure the <quantum typical subspace> projector $\Pi$. Encode its successful sector isometrically and reserve one orthogonal compressed flag for failure; decode the flag to a fixed state. The composite channel is $\mathcal N_n(\tau)=\Pi\tau\Pi+\operatorname{Tr}[(I-\Pi)\tau]|\varphi_0\rangle\langle\varphi_0|$. It is trace preserving. The <Kraus formula for entanglement fidelity> gives the displayed lower bound, while convexity of the square gives the same bound for average pure-source fidelity. One flag adds only a vanishing asymptotic rate overhead.
Back to article page
