  Stokes vectors and Discrete Wigner functions (DWF) provide two alternate ways
of representing the polarization state of multiphoton systems. The Stokes
vector associated with a n-photon polarization state is unique, and its
Minkowski squared norm provides a direct way of quantifying entanglement
through n-concurrence. However, the quantification of entanglement from DWF is
not straight forward. The DWF associated with a given quantum state is not
unique but depends on the way in which basis vectors are assigned to various
lines in the phase space. For a Hilbert space of dimension N, there exists N
N+1 such possible assignments. While a given DWF corresponds to a unique Stokes
vector, the converse is not true. In the present work, we show that, for each
particular assignment called a quantum net, there exist a unique Hadamard
matrix which relates the Stokes vector to the corresponding DWF. This method
provides an elegant and direct method of constructing the DWFs from the Stokes
vector for every possible choice of the quantum net. Using these results, we
derive the relationship between the Stokes vector of a spin-flipped state and
the DWF. Finally, we also present a method to express the Minkowskian squared
norm of the Stokes vector directly in terms of the DWF.
