Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data

• URL: http://arxiv.org/abs/2506.22092v1
• Date: Fri, 27 Jun 2025 10:24:37 GMT
• Title: Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data
• Authors: Andreu Riera-Campeny, Patrick Maurer, Oriol Romero-Isart,
• Abstract summary: We propose a hypothesis testing framework that distinguishes between classical and quantum mechanics based on position measurements.<n>We show that the likelihood ratio test provides an exponential reduction in measurements needed to reach a given confidence level.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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