the transition probabilities. Appendix B proves a technical result useful for characterizing those sets of transition rates that represent Hamiltonian dynamics.

Discrete Wigner function
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For our analysis we use the discrete Wigner function defined in Ref. [@Wootters1987]. That Wigner function is simplest when the dimension of the Hilbert space is a prime number, and for simplicity in the present paper, we restrict our attention to that case. (When the state-space dimension is composite, the system is, in effect, treated as a composite object.)

The discrete phase space can be pictured as an $N \times N$ array of points, where $N$ is the dimension of the system’s Hilbert space. We will use Greek letters to label the points of phase space, and for the point $\alpha = (\alpha_1, \alpha_2)$, we will picture $\alpha_1$ and $\alpha_2$ as the horizontal and vertical coordinates, respectively, where each $\alpha_i$ takes the values $0, 1, \ldots, N-1$. Because $N$ is prime, these values, together with the operations of addition and multiplication mod $N$, constitute a finite field. With the coordinate labels understood as elements of this field, the phase space acquires the structure of a toroidal array. In this phase space one can identify exactly 