  Time reversal and spin flip are discrete symmetry operations of substantial
import to quantum information and quantum computation. Spin flip arises in the
context of separability, quantification of entanglement and the construction of
Universal NOT gates. The present work investigates the relationship between the
quantum state of a multiqubit system represented by the Discrete Wigner
Function (DWFs) and its spin-flipped counterpart. The two are shown to be
related through a Hadamard matrix that is independent of the choice of the
quantum net used for the tomographic reconstruction of the DWF. These results
would be of interest to cases involving the direct tomographic reconstruction
of the DWF from experimental data and in the analysis of entanglement related
properties purely in terms of the Discrete Wigner function.
