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Ideal stochastic process modeling with post-quantum quasiprobabilistic theories

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Researchers demonstrated that classical and quantum models cannot achieve the fundamental memory limit—excess entropy—for simulating stochastic processes, requiring more information storage than the past-future mutual information shared. The team introduced "n-machines," a post-quantum generalization of hidden Markov models using negative quasiprobabilities, which can saturate the excess entropy bound under collision entropy measures. Negativity in quasiprobabilities emerges as a computational resource, enabling memory efficiency beyond classical and quantum systems, suggesting a new paradigm for stochastic process modeling. The study builds on prior work linking negative probabilities to quantum advantage, extending it to memory optimization in complex dynamical systems. This breakthrough could redefine information processing limits, offering a framework for ultra-efficient simulations in fields like AI, thermodynamics, and quantum machine learning.

Ideal stochastic process modeling with post-quantum quasiprobabilistic theories

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AbstractIn 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.► BibTeX data@article{Onggadinata2026idealstochastic, doi = {10.22331/q-2026-02-23-2005}, url = {https://doi.org/10.22331/q-2026-02-23-2005}, title = {Ideal stochastic process modeling with post-quantum quasiprobabilistic theories}, author = {Onggadinata, Kelvin and Tanggara, Andrew and Gu, Mile and Kaszlikowski, Dagomir}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2005}, month = feb, year = {2026} }► References [1] L. Rabiner and B. Juang. ``An introduction to hidden Markov models''. IEEE ASSP Magazine 3, 4–16 (1986). https://doi.org/10.1109/MASSP.1986.1165342 [2] M. Vidyasagar. ``Hidden Markov processes: Theory and applications to biology''.

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In Complex Sciences. Pages 265–276. Berlin, Heidelberg (2009).

In Harald Atmanspacher and Gerhard J. Dalenoort, editors, Inside Versus Outside. Pages 235–272. Berlin, Heidelberg (1994).

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