Recovery metrics and finite-coupling lower bounds

For a selected packet channel $\mathcal{N}$, define

For a qubit density $\rho$, choose a purification $|{\psi }_{\rho }⟩$ and put

Its value is independent of the purification convention. This is squared worst-case entanglement fidelity against identity.

The general recovery/environment literature treats metric-specific duality and continuity BenyOreshkov,KSW. The constants below are instead derived directly for the present qubit input.