Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data

TL;DR

This paper introduces a hypothesis testing framework using likelihood ratios to efficiently certify quantum behavior in macroscopic particles, reducing experimental requirements compared to traditional interference visibility methods.

Contribution

It proposes a likelihood ratio test approach that leverages full probability distributions to distinguish quantum from classical mechanics more efficiently.

Findings

Likelihood ratio test reduces measurement count exponentially.

Method provides a more efficient way to falsify classical mechanics.

Applicable to macroscopic superposition experiments.

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.