Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914589062463488 |
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| author | Riera-Campeny, Andreu Maurer, Patrick Romero-Isart, Oriol |
| author_facet | Riera-Campeny, Andreu Maurer, Patrick Romero-Isart, Oriol |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data Riera-Campeny, Andreu Maurer, Patrick Romero-Isart, Oriol Quantum Physics 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. |
| title | Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.22092 |