Stokes vector and its relationship to Discrete Wigner Functions of multiqubit states

• Relationship between Stokes vector (SV) and discrete Wigner function (DWF) for arbitrary multiqubit states is presented.
• It is shown that SV and DWF are related to one another through Hadamard matrices.
• We show that the Hadamard matrices depend on the choice of the quantum net.
• Relationship between SV of the spin flipped state and the DWF is derived.
• Expression to compute n-concurrence of the pure n-qubit systems purely in terms of DWF is given.

A Stokes vectors and Discrete Wigner Functions (DWF) provide two alternate ways of representing the state of multiqubit systems. A general relationship between the Stokes vector and the DWF is derived for arbitrary n-qubit states for all possible choices of quantum nets. The Stokes vector and the DWF are shown to be related through a Hadamard Matrix. Using these results, a relationship between the Stokes vector of a spin-flipped state and the DWF is derived. Finally, we also present a method to express the Minkowskian squared norm of the Stokes vector, corresponding to n-concurrence in terms of the DWF.