Remark: Purity endpoints

At $\eta =0$, the accessible subsystem is pure vacuum for every message, but the optimal recovery error is $3/4$. At $\eta =1$, a Bell input produces an accessible marginal $W(I_2/2)W^{†}$ of purity $1/2$, but recovery is exact.

At full transfer the residual subsystem is pure vacuum. That purity certifies neither residual recovery nor global loss: the message has moved to $R$.