Proposition: Referenced dephasing is not specified by its marginal

For Bell input $|\Phi ⟩=(|00⟩+|11⟩)/\sqrt{2}$, the accessible one-qubit marginal under ${\Lambda }_{\lambda }$ is $I_2/2$ for every $\lambda \in [0,1]$. The joint state is

Its partial-transpose spectrum is

so its negativity is $\lambda /2$.

The optimal deterministic recovery error is

Proof. Partial trace and partial transpose give the stated matrices. For recovery, the two noisy $X$-eigenstate outputs have trace distance $\lambda$. Any decoder of half-diamond error $e$ must satisfy $1\le \lambda +2e$, by contraction and the triangle inequality. Identity decoding attains $e=(1-\lambda )/2$ using (eq:dephchannel).