Generating Mutually Unbiased Bases and Discrete Wigner Functions for Three-Qubit System

It is known that there exists 2(N) + 1 mutually unbiased bases for N qubits system. Between the different MUB construction algorithms of the three-qubit case, we focus on Wootters method with discrete phase space that leads naturally to a complete set of 2(N) + 1 mutually unbiased bases for the state space. We construct discrete Wigner function using mutually unbiased bases from the discrete phase space for three-qubit system by explicitly calculating the Wigner functions for exemplary three-qubit pure states such as the GHZ state, the W state and the embedded Bell state. We also highlight some quasi-probability characteristics of these entangled states.