Consider Wigner function representation of a qubit in the basis labeled by $\sigma_z$ and $\sigma_x$ eigenvalues. A general single qubit mixed state has the Bloch representation,$\rho = 1/2 (I + r.\sigma)$with $|r| ≤ 1$. Find the region of the Bloch sphere such that each element of its Wigner function is positive.
In this problem how can we evaluate the wigner function as we know that wigner function is one of the density matrices?
