that the particles’ momenta will undergo the specified shifts. These transition rates, like the Wigner function itself, can be negative, so one cannot interpret the equation as literally representing a probabilistic process in the usual sense. Elsewhere in the paper, though, Wigner observes that one will be able to obtain valid results by manipulating negative probabilities mathematically just as one would manipulate ordinary probabilities. Several decades later, Feynman similarly argued that one should not automatically rule out the use of negative probabilities, again because the end result can be perfectly sensible even if certain intermediate steps are difficult if not impossible to interpret [@Feynman1987a].

The original Wigner function has now been extended, in a few different ways, to systems with a finite-dimensional Hilbert space, for which the phase space is a discrete lattice [@Buot1974; @Hannay1980; @Wootters1987; @Galetti1988; @Cohendet1988; @Cohendet1990; @Leonhardt1995; @Leonhardt1996; @Vourdas1996; @Luis1998DiscreteSystems; @Hakioglu1998; @Rivas1999; @Gibbons2004; @Vourdas2004; @Klimov2005a; @Gross2006; @Gross2007; @Vourdas2013]. Such discrete Wigner functions have found interesting applications in studies of entanglement characterization [@Franco2006], quantum teleportation [@Koniorczyk2001; @Paz2002], quantum algorithms [@Bianucci2002; @Miquel2002; @Miquel2002a], quantum computation [@Galvao2005; @Cormick2006], error-correcting codes [@Paz2005] and quantum state tomography [@Marchiolli2005; @Wootters2004]. As with the continuous Wigner function, the evolution of the discrete Wigner function 