Quasiprobability as a resource for memory reduction in stochastic process modeling

Abstract: In stochastic modeling, the excess entropy -- the mutual information shared between a processes past and future -- represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated by either classical machines or their enhanced quantum counterparts. Simulating a process fundamentally requires us to store more information in the present than what is shared between past and future. Here we consider a hypothetical generalization of hidden Markov models beyond classical and quantum models, referred as n-machines, that allow for negative quasiprobabilities. We show that under the collision entropy measure of information, the minimal memory of such models can equalize the excess entropy. Our results hint negativity as a necessary resource for memory-advantaged stochastic simulation -- mirroring similar interpretations in various other quantum information tasks.