Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data

Abstract:We address the challenge of certifying quantum behavior with single macroscopic massive particles, subject to decoherence and finite data. We propose a hypothesis testing framework that distinguishes between classical and quantum mechanics based on position measurements. While interference pattern visibility in single-particle quantum superposition experiments has been commonly used as a sufficient criterion to falsify classical mechanics, we show that, from a hypothesis testing perspective, it is neither necessary nor efficient. Focusing on recent proposals to prepare macroscopic superposition states of levitated nanoparticles, we show that the likelihood ratio test -- which leverages differences across the entire probability distribution -- provides an exponential reduction in measurements needed to reach a given confidence level. These results generalize to a broad class of quantum states, and offer a principled, efficient method to falsify classical mechanics in interference experiments, relaxing the experimental constraints faced by current efforts to test quantum mechanics at the macroscopic scale.

arXiv:2506.22092 [quant-ph]

(or arXiv:2506.22092v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2506.22092 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. Research 8, 023196 (2026)

https://doi.org/10.1103/gttg-mvrq Focus to learn more DOI(s) linking to related resources

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