Generating mutually unbiased bases and discrete wigner functions for three-qubit system

It is known that there exists 2n + 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 2n + 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.