Example: Why low leakage is not a freshness theorem

Consider an exact first-session interface

The logical complement is replacement and has zero leakage. Nevertheless $M$ is correlated with $S$.

If $S$ is discarded after returning $A$, then the accessible resource ${\Phi }_{SM}$ is gone. The remaining marginal $I_M/h$ does not restore it. A proposed second teleportation session cannot replace a missing receiver half by the fact that this marginal is unchanged.

More generally, a Bell state on $QM$ and the product state $I_Q/h\otimes I_M/h$ have identical $M$ marginals but trace distance $1-h^{-2}$. Marginal equality does not establish a reference-preserving reset.