It has been shown in earlier works that the vertices of Platonic solids are
good measurement choices for tests of EPR-steering using isotropically
entangled pairs of qubits. Such measurements are regularly spaced, and
measurement diversity is a good feature for making EPR-steering inequalities
easier to violate in the presence of experimental imperfections. However, such
measurements are provably suboptimal. Here, we develop a method for devising
optimal strategies for tests of EPR-steering, in the sense of being most robust
to mixture and inefficiency (while still closing the detection loophole of
course), for a given number n of measurement settings. We allow for arbitrary
measurement directions, and arbitrary weightings of the outcomes in the
EPR-steering inequality. This is a difficult optimization problem for large
n, so we also consider more practical ways of constructing near-optimal
EPR-steering inequalities in this limit.Comment: 15 pages, 11 Figure
