  We find that the perfect distinguishability of two quantum operations by a
parallel scheme depends only on an operator subspace generated from their
Choi-Kraus operators. We further show that any operator subspace can be
obtained from two quantum operations in such a way. This connection enables us
to study the parallel distinguishability of operator subspaces directly without
explicitly referring to the underlining quantum operations. We obtain a
necessary and sufficient condition for the parallel distinguishability of an
operator subspace that is either one-dimensional or Hermitian. In both cases
the condition is equivalent to the non-existence of positive definite operator
in the subspace, and an optimal discrimination protocol is obtained. Finally,
we provide more examples to show that the non-existence of positive definite
operator is sufficient for many other cases, but in general it is only a
necessary condition.
