N$ matrices, so that we can write any such matrix as a linear combination of the $\hat{A}$’s. In particular, we can invert Eq. (\[W\]): $$\hat{\rho} = \sum_\alpha W_\alpha \hat{A}_\alpha.$$ That is, the values of the Wigner function are simply the coefficients in the expansion of $\hat{\rho}$ in the phase point operators. Meanwhile the first and third of the above statements imply the following properties of the Wigner function.

> \(i) $\sum_\alpha W_\alpha = 1$.

> \(ii) The sums of $W_\alpha$ over the lines of a striation are the probabilities of the outcomes of the orthogonal measurement associated with that striation.

These properties, which are analogous to properties of the continuous Wigner function, provide a sense in which the discrete Wigner function acts like a probability distribution: the Wigner function is normalized like a probability distribution, and the marginal distribution over each direction in phase space is an actual, non-negative probability distribution, corresponding to a complete orthogonal measurement. But like the continuous Wigner function, $W_\alpha$ can take negative values. Indeed, for the case $N=2$, the Wigner function we are using is essentially the same as a function Feynman defined in one of his examples of negative probabilities [@Feynman1987a].

Not every normalized 