  In this paper we pose the question of how one can quantify the amount of
entanglement necessary to create a given steering assemblage, when the original
state and measurements are unknown. To do this, we extend the concepts of
entanglement cost and entanglement of formation to steering assemblages, and
show how to upper bound them with semidefinite programming. We prove that the
entanglement of formation for assemblages is not generally continuous and not a
flat roof extension; and use numerical analysis to illustrate these properties.
Finally, we discuss the consequences of these results for
assemblage-to-assemblage conversion and directions for further research.
