  Based on the general form of entanglement witnesses constructed from
separable states, we first show a sufficient condition of violating the
structural physical approximation (SPA) conjecture [Phys. Rev. A 78, 062105
(2008)]. Then we discuss the SPA conjecture for decomposable entanglement
witnesses. Moreover, we make geometric illustrations of the connection between
entanglement witnesses and the sets of quantum states, separable states, and
entangled states comparing with planes and vectors in Euclidean space.
