Ideal stochastic process modeling with post-quantum quasiprobabilistic theories

Abstract

In stochastic modeling, the excess entropy -- the mutual information shared between a process's 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 is shared between the past and the future. Here, we consider a generalization of hidden Markov models beyond classical and quantum models, referred to 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 equal the excess entropy. Our results suggest that negativity can be a useful resource for achieving nonclassical memory advantage.

29 pages, 15 figures, updated title. Accepted in Quantum (2026-01-31)