  The resource theories of separable entanglement, non-positive partial
transpose entanglement, magic, and imaginarity share an interesting property:
An operation is free if and only if its renormalized Choi matrix is a free
state. In this letter, we refer to resource theories exhibiting this property
as Choi-defined resource theories. We demonstrate how and under what conditions
one can construct a Choi-defined resource theory, and we prove that when such a
construction is possible, the free operations are all and only the completely
resource non-generating operations.
