  We study the entanglement-breaking (EB) space, such that the entanglement of
formation (EOF) of a bipartite quantum state is additive when its range is an
EB subspace. We systematically construct the EB spaces in the Hilbert space
$\bbC^m\otimes\bbC^3$, and the $2$-dimensional EB space in
$\bbC^2\otimes\bbC^n$. We characterize the expression of two-qubit states of
rank two with nonadditive EOF, if they exist. We further apply our results to
construct EB spaces of an arbitrarily given dimensions. We show that the
example in [PRL 89,027901(2002)] is a special case of our results. We further
work out the entanglement cost of a qubit-qutrit state in terms of the two-atom
system of the .
