  We consider the smallest possible directional reference frames allowed and
determine the best one can ever do in preserving quantum information in various
scenarios. We find that for the preservation of a single spin state, two
orthogonal spins are optimal primitive reference frames, and in a product state
do approximately 22% as well as an infinite-sized classical frame. By adding a
small amount of entanglement to the reference frame this can be raised to
2(2/3)^5 = 26%. Under the different criterion of entanglement-preservation a
very similar optimal reference frame is found, however this time for spins
aligned at an optimal angle of 87 degrees. In this case 24% of the negativity
is preserved. The classical limit is considered numerically, and indicates
under the criterion of entanglement preservation, that 90 degrees is selected
out non-monotonically, with a peak optimal angle of 96.5 degrees for L = 3
spins.
