Ideal stochastic process modeling with post-quantum quasiprobabilistic theories

TL;DR

This paper introduces n-machines, a generalized stochastic model allowing negative quasiprobabilities, demonstrating that negativity can enable models to match the minimal memory bound set by excess entropy, surpassing classical and quantum limits.

Contribution

It proposes a new class of models called n-machines that utilize negativity to achieve optimal memory efficiency in stochastic processes, surpassing classical and quantum models.

Findings

n-machines can match the excess entropy bound using negativity.

Negativity acts as a resource for nonclassical memory advantage.

Models with negativity can minimize memory requirements to fundamental limits.

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.