Occam's Quantum Razor: How Quantum Mechanics can reduce the complexity of classical models

TL;DR

This paper demonstrates that quantum models can reduce the complexity of classical stochastic models by requiring less input information, revealing potential for simpler representations of phenomena through quantum effects.

Contribution

It introduces a systematic method to construct quantum models that outperform classical models in terms of informational efficiency for stochastic processes.

Findings

Quantum models can break classical informational bounds.

Minimal entropy quantum models necessarily involve quantum dynamics.

Many phenomena could be simpler to model with quantum effects.

Abstract

Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of Occam's razor, simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. We systematically construct quantum models that break this classical bound, and show that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved.