Proposition: A direct non-identification check

The channel ${\mathcal{A}}_{1/2,1/4}$ is not entanglement breaking.

Proof. The partial transpose of (eq:choi) contains the principal block

whose determinant is

It is therefore not positive. Every separable positive operator has positive partial transpose, so the Choi operator is entangled. An entanglement-breaking channel would send half of a maximally entangled input to a separable Choi state HSR.