We characterize a convex subset of entanglement witnesses for two qutrits.
Equivalently, we provide a characterization of the set of positive maps in the
matrix algebra of 3 x 3 complex matrices. It turns out that boundary of this
set displays elegant representation in terms of SO(2) rotations. We conjecture
that maps parameterized by rotations are optimal, i.e. they provide the
strongest tool for detecting quantum entanglement. As a byproduct we found a
new class of decomposable entanglement witnesses parameterized by improper
rotations from the orthogonal group O(2).Comment: 9 page
