  Visual Cryptography Schemes (VCS) based on the "XOR" operation (XVCS) exhibit
significantly smaller pixel expansion and higher contrast compared to those
based on the "OR" operation. Moreover, the "XOR" operation appears to possess
superior qualities, as it effectively operates within a binary field, while the
"OR" operation merely functions as a ring with identity. Despite these
remarkable attributes, our understanding of XVCS remains limited. Especially,
we have done little about the noise in the reconstructed image up to now. In
this paper, we introduce a novel concept called Static XVCS (SXVCS), which
completely eliminates the noise in the reconstructed image. We also demonstrate
that the equivalent condition for perfect white pixel reconstruction is simply
the existence of SXVCS. For its application, we naturally propose an efficient
method for determining the existence of XVCS with perfect white pixel
reconstruction. Furthermore, we apply our theorem to $(2,n)$-XVCS and achieve
the optimal state of $(2,n)$-XVCS.
