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  • Open Access

Certifying macroscopic quantum mechanics via hypothesis testing with finite data

Andreu Riera-Campeny1,2,*, Patrick Maurer2, and Oriol Romero-Isart1,3

  • *Contact author: andreu.riera-campeny@icfo.eu
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Phys. Rev. Research 8, 023196 – Published 21 May, 2026

DOI: https://doi.org/10.1103/gttg-mvrq

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.

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Outline

Information

Phys. Rev. Research 8, 023196– Published 21 May, 2026
  • Received 4 July 2025
  • Accepted 27 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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