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In a recent paper, Buniy et al. have argued that a possible discretization ofspacetime leads to an unavoidable discretization of the state space of quantummechanics. In this paper, we show that this conclusion is not limited toquantum theory: in any classical, quantum, or more general probabilistictheory, states (i.e. probabilities or corresponding amplitudes) become discreteor fuzzy for observers, as long as time evolution is reversible and entropy islocally bounded.  Specifically, we show that the Bekenstein bound suggests that probabilitiesin small closed regions of space carry an uncertainty inversely proportional tothe the square root of the system's effective radius and energy.

Does Probability become Fuzzy in Small Regions of Spacetime?